Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na
Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Cover of the book
Tytuł książki

On the reflexivity of multigenerator algebras



Rozprawy Matematyczne tom/nr w serii: 378 wydano: 1998


Warianty tytułu


1. Introduction...................................................................................................5
2. N-tuples of linear transformations in finite-dimensional space......................8
3. Toeplitz operators on the polydisc and the unit ball....................................18
4. Subspaces of weighted shifts.....................................................................23
5. Joint spectra for N-tuples of operators........................................................27
6. Algebras of operator weighted shifts...........................................................30
7. Functional calculus for N-tuples of contractions..........................................37
8. Dual algebras, invariant subspace problem and reflexivity..........................44
9. Reflexivity of jointly quasinormal operators and spherical isometries..........45
10. Reflexivity and existence of invariant subspaces......................................47
11. Questions and open problems..................................................................56

Miejsce publikacji




Rozprawy Matematyczne tom/nr w serii: 378

Liczba stron


Liczba rozdzia³ów

Opis fizyczny

Dissertationes Mathematicae, Tom CCCLXXVIII




  • Institute of Mathematics, University of Agriculture, Ul. Królewska 6, 30-045 Kraków, Poland


  • [AC] E. Albrecht and B. Chevreau, Invariant subspaces for certain representations of $H^∞(G)$, in: Functional Analysis, K. Bierstedt, A. Pietsch, W. Ruess and E. Vogt (eds.), Marcel Dekker, New York, 1993 293-305.
  • [AP] E. Albrecht and M. Ptak, Invariant subspaces for doubly commuting contractions with rich Taylor spectrum, J. Operator Theory (to appear).
  • [AF] F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer, New York, 1974.
  • [Ap] C. Apostol, Functional calculus and invariant subspaces, J. Operator Theory 4 (1980) 159-190.
  • [Az] E. A. Azoff, On finite rank operators and preannihilators, Mem. Amer. Math. Soc. 357 (1986).
  • [AFG] E. A. Azoff C. K. Fong and F. Gilfeather, A reduction theory for non-self-adjoint operator algebras, Trans. Amer. Math. Soc. 224 (1976) 351-366.
  • [AP1] E. A. Azoff and M. Ptak, On the rank-two linear transformations and reflexivity, J. London Math. Soc. 53 (1996) 383-396.
  • [AP2] E. A. Azoff and M. Ptak, Jointly quasinormal families are reflexive, Acta Sci. Math. (Szeged) 61 (1995) 545-547.
  • [AP3] E. A. Azoff and M. Ptak, Reflexive closure of space of Toeplitz operators, preprint.
  • [AP4] E. A. Azoff and M. Ptak, A dichotomy for linear spaces of Toeplitz operators, J. Funct. Anal. (to appear).
  • [AS] E. A. Azoff and H. A. Shehada, Literal embeddings of linear spaces of operators, Indiana Univ. Math. J. 42 (1993) 571-589.
  • [Bk1] O. B. Bekken, Product of algebras on plane sets, U.C.L.A. thesis, 1972.
  • [Bk2] O. B. Bekken, Rational approximation on product sets, Trans. Amer. Math. Soc. 191 (1974) 301-316.
  • [Berb] S. K. Berberian, Notes on Spectral Theory, Van Nostrand, Princeton, 1966.
  • [Ber] H. Bercovici, A factorization theorem with applications to invariant subspaces and reflexivity of isometries, Math. Res. Lett. 1 (1994), 511-518.
  • [BCFP] H. Bercovici, B.Chevreau, C. Foiaş and C. Pearcy, Dilation theory and systems of simultaneous equations in the predual of an operator algebra, II, Math. Z. 189 (1984) 97-103.
  • [BFLP] H. Bercovici, C. Foiaş, J. Langsam and C. Pearcy, (BCP)-Operators are reflexive, Michigan Math. J. 29 (1982) 371-379.
  • [BFP1] H. Bercovici C. Foiaş and C. Pearcy, Dilation theory and systems of simultaneous equations in the predual of an operator algebra, I, Michigan Math. J. 30 (1983) 335-354.
  • [BFP2] H. Bercovici C. Foiaş and C. Pearcy, Dual Algebras with Applications to Invariant Subspaces and Dilation Theory, CBMS Regional Conf. Ser. in Math. 56, Amer. Math. Soc., Providence, 1985.
  • [BW] H. Bercovici and D. Westwood, The factorization of functions in the polydisc, Houston J. Math. 18 (1992) 1-6.
  • [BDO] E. Breim A. M. Davie and B. K. Øksendal, Functional calculus for commuting contractions, J. London Math. Soc. 7 (1973) 709-718.
  • [BF] L. Brickman and P. A. Fillmore, The invariant subspace lattice of the linear transformation, Canad. J. Math. 19 (1967) 810-822.
  • [BP] A. Brown and C. Pearcy, Compact restrictions of operators, Acta Sci. Math. (Szeged) 33 (1971) 271-282.
  • [Br] S. Brown, Some invariant subspaces for subnormal operators, Integral Equations Operator Theory 1 (1978) 310-330.
  • [BCP1] S. Brown B. Chevreau and C. Pearcy, Contractions with rich spectrum have invariant subspaces, J. Operator Theory 1 (1979) 123-136.
  • [BCP2] S. Brown B. Chevreau and C. Pearcy, On the structure of contraction operators, II, J. Funct. Anal. 76 (1988) 30-55.
  • [CEP] B. Chevreau G. Exner and C. Pearcy, On the structure of contraction operators, III, Michigan Math. J. 36 (1989) 29-62.
  • [CP1] B. Chevreau and C. Pearcy, On the structure of contraction operators with applications to invariant subspces, J. Funct. Anal. 67 (1986) 360-379.
  • [CP2] B. Chevreau and C. Pearcy, On the structure of contraction operators, I, J. Funct. Anal. 76 (1988) 1-29.
  • [CPS] B. Chevreau C. Pearcy and A. L. Shields, Finitely connected domains G, representations of $H^∞(G)$, and invariant subspaces, J. Operator Theory 6 (1981) 375-405.
  • [CG] B. J. Cole and T. W. Gamelin, Tight uniform algebras of analytic functions, J. Funct. Anal. 46 (1982) 158-220.
  • [Cu1] R. Curto, Fredholm and invertible n-tuples of operators. The deformation problem, Trans. Amer. Math. Soc. 266 (1981) 129-159.
  • [Cu2] R. Curto, Applications of several complex variables to multiparameter spectral theory, in: Survey of Recent Results in Operator Theory, Vol. II, J. B. Conway and B. B. Morrel (eds.), Longman, London, 1988 25-90.
  • [Da] A. T. Dash, Joint spectra, Studia Math. 45 (1973) 225-237.
  • [DJ] A. M. Davie and N. P. Jewell, Toeplitz operators in several complex variables, J. Funct. Anal. 26 (1977) 356-368.
  • [De] J. A. Deddens, Every isometry is reflexive, Proc. Amer. Math. Soc. 28 (1971) 509-511.
  • [DF] J. A. Deddens and P. A. Fillmore, Reflexive linear transformations, Linear Algebra Appl. 10 (1975) 89-93.
  • [D1] L. Ding, Separating vectors and reflexivity, Linear Algebra Appl. 174 (1992) 37-52.
  • [D2] L. Ding, An algebraic reflexivity result, Houston J. Math. 19 (1993) 533-540.
  • [Do] R. G. Douglas, Banach Algebra Techniques in Operator Theory, Academic Press, 1972.
  • [En] M. Engliš, Density of the algebras generated by Toeplitz operators on Bergman spaces, Ark. Mat. 30 (1992) 227-243.
  • [E1] J. Eschmeier, Representations of $H^∞(G)$ and invariant subspaces, Math. Ann. 298 (1994) 167-186.
  • [E2] J. Eschmeier, C₀₀-representations of $H^∞(G)$ with dominating Harte spectrum, preprint.
  • [FSW] P. A. Fillmore J. G. Stampfli and J.~P. Williams, On the essential numerical range, the essential spectrum, and a problem of Halmos, Acta Sci. Math. (Szeged) 32 (1972) 179-192.
  • [G] T. W. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Clifs, N.J., 1969.
  • [Had] D. Hadwin, Algebraically reflexive linear transformations, Linear Multilinear Algebra 14 (1983) 225-233.
  • [HN1] D. Hadwin and E. A. Nordgren, Subalgebras of reflexive algebras, J. Operator Theory 7 (1982) 3-23.
  • [HN2] D. Hadwin and E. A. Nordgren, Reflexivity and direct sums, Acta Sci. Math. (Szeged) 55 (1991) 181-197.
  • [HK] D. Hadwin and J. W. Kerr, Scalar-reflexive rings, Proc. Amer. Math. Soc. 103 (1988) 1-8.
  • [Ha] P. R. Halmos, A Hilbert Space Problem Book, Van Nostrand, 1967.
  • [Ho] K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, Englewood Cliffs, N.J., 1962.
  • [HM] K. Horák and V. Müller, On commuting isometries, Czechoslovak Math. J. 43 (118) (1993) 373-382.
  • [Hw] A. Hwang, On a theorem of Brickman-Fillmore, Proc. Amer. Math. Soc. 55 (1976) 93-94.
  • [Iz] K. Izuchi, Unitary equivalence of invariant subspaces in the polydisc, Pacific J. Math. 130 (1987) 351-358.
  • [J] N. P. Jewell, Multiplication by the coordinate functions on the Hardy space of the unit sphere in $ℂ^N$, Duke Math. J. 44 (1977) 839-851.
  • [JL] N. P. Jewell and A. R. Lubin, Commuting weighted shifts and analytic function theory in several variables, J. Operator Theory 1 (1979) 207-223.
  • [K] I. Kaplansky, Infinite Abelian Groups, Univ. of Michigan Press, Ann Arbor, 1954.
  • [KS] H. Konig and G. Seever, The abstract F. and M. Riesz theorem, Duke Math. J. 17 (1965), 139-146.
  • [K1] M. Kosiek, Lebesgue-type decomposition of a pair of commuting Hilbert space operators, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979) 583-589.
  • [K2] M. Kosiek, Representation generated by a finite number of Hilbert space operators, Ann. Polon. Math. 44 (1984) 309-315.
  • [KOP] M. Kosiek A. Octavio and M. Ptak, On the reflexivity of pairs of contractions, Proc. Amer. Math. Soc. 123 (1995) 1229-1236.
  • [KP] M. Kosiek and M. Ptak, Reflexivity of N-tuples of contractions with rich joint left essential spectrum, Integral Equations Operator Theory 13 (1990) 395-420.
  • [Kr] S. G. Krantz, Function Theory of Several Complex Variables, Wiley, New York, 1982.
  • [La] A. Lambert, The algebra generated by an invertibly weighted shift, J. London Math. Soc. (2) 5 (1972) 741-747.
  • [LC] W. S. Li and J. McCarthy, Reflexivity of isometries, Studia Math. 124 (1997) 101-105.
  • [LS] W. S. Li and E. Strouse, Reflexivity of tensor products of linear transformations, Proc. Amer. Math. Soc. 123 (1995) 2021-2030.
  • [LSu] A. I. Loginov and V. I. Sulman, On hereditary and intermediate reflexivity of W* algebras, Soviet Math. Dokl. 14 (1973) 1473-1476.
  • [Lu] A. Lubin, Weighted shifts and commuting normal extentions, J. Austral. Math. Soc. Ser. A 27 (1979) 17-26.
  • [MP] V. Müller and M. Ptak, Spherical isometries are hyporeflexive, Rocky Mountain J. Math. (to appear).
  • [Oc] A. Octavio, Coisometric extension and functional calculus for pairs of commuting contractions, J. Operator Theory 31 (1994) 67-82.
  • [OT] R. Olin and J. Thomson, Algebras of subnormal operators, J. Funct. Anal. 37 (1980) 271-301.
  • [Pa] S. Parrot, Unitary dilation for commuting contractions, Pacific J. Math. 34 (1970) 481-490.
  • [P1] M. Ptak, On the reflexivity of pairs of isometries and of tensor products for some reflexive algebras, Studia Math. 37 (1986) 47-55.
  • [P2] M. Ptak, Reflexivity of pairs of shifts, Proc. Amer. Math. Soc. 109 (1990) 409-415.
  • [P3] M. Ptak, Reflexivity of multiplication operators in certain domains in $ℂ^N$, Bull. Polish Acad. Sci. Math. 37 (1989) 217-220.
  • [P4] M. Ptak, The algebra generated by a pair of operator weighted shifts, Ann. Polon. Math. 62 (1995) 97-110.
  • [RR] H. Radjavi and P. Rosenthal, Invariant Subspaces, Springer, New York, 1973.
  • [Ro1] G. Robel, On the structure of (BCP)-operators and related algebras I, J. Operator Theory 12 (1984) 23-45.
  • [Ro2] G. Robel, On the structure of (BCP)-operators and related algebras II, J. Operator Theory 12 (1984) 235-245.
  • [Ru1] W. Rudin, Function Theory in Polydiscs, Benjamin, New York, 1969.
  • [Ru2] W. Rudin, Function Theory in the Unit Ball of ℂⁿ, Springer, New York, 1980.
  • [Ru3] W. Rudin, New Constructions of Functions Holomorphic in the Unit Ball of ℂⁿ, CBMS Regional Conf. Ser. in Math. 63, Amer. Math. Soc., Providence, 1986.
  • [Rud] K. Rudol, On spectral mapping theorem, J. Math. Anal. Appl. 97 (1983) 131-193.
  • [Sa] D. Sarason, Invariant subspaces and unstarred operator algebras, Pacific J. Math. 17 (1966) 511-517.
  • [Sw] J. T. Schwartz, W*-algebras, Gordon and Breach, New York, 1967.
  • [Sh] A. L. Shields, Weighted shift operators and analytic function theory, in: Math. Surveys 13, Amer. Math. Soc., 1974 49-128.
  • [SW] A. L. Shields and L. J. Wallen, The commutant of certain Hilbert space operators, Indiana Univ. Math. J. 20 (1971) 777-788.
  • [Sł1] M. Słociński, Isometric dilation of doubly commuting contractions and related models, Bull. Acad. Polon. Sci. 25 (1977) 1233-1242.
  • [Sł2] M. Słociński, On the Wold-type decomposition of a pair of commuting isometries, Ann. Polon. Math. 37 (1980) 255-262.
  • [SNF] B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, 1970.
  • [T1] J. L. Taylor, A joint spectrum of several commuting operators, J. Funct. Anal. 6 (1970) 172-191.
  • [T2] J. L. Taylor, The analytic functional calculus for several commuting operators, Acta Math. 125 (1970) 1-38.
  • [We] D. Westwood, On C₀₀ contractions with dominating spectrum, J. Funct. Anal. 66 (1982) 96-104.
  • [W] W. R. Wogen, Quasinormal operators are reflexive, Bull. London Math. Soc. (2) 31 (1979) 19-22.
  • [Ya] K. Yan, Invariant subspaces for jointly subnormal systems, preprint.

Języki publikacji



1991 Mathematics Subject Classification: Primary 47D27, 47A15; Secondary 15A30, 47D25, 47D15, 47B37, 47B35, 47B20.

Identyfikator YADDA





Zawartość książki

rozwiń roczniki

JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.