PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1999 | 137 | 2 | 177-194
Tytuł artykułu

Pointwise multiplication operators on weighted Banach spaces of analytic functions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For a wide class of weights we find the approximative point spectrum and the essential spectrum of the pointwise multiplication operator $M_φ$, $M_φ(f)=φf$, on the weighted Banach spaces of analytic functions on the disc with the sup-norm. Thus we characterize when $M'_φ$ is Fredholm or is an into isomorphism. We also study cyclic phenomena for the adjoint map $M'_φ$.
Czasopismo
Rocznik
Tom
137
Numer
2
Strony
177-194
Opis fizyczny
Daty
wydano
1999
otrzymano
1999-01-07
poprawiono
1999-08-23
Twórcy
autor
  • Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, E-46071 Valencia, Spain , jbonet@pleione.cc.upv.es
autor
  • Institute of Mathematics (Poznań branch), Polish Academy of Sciences, Matejki 48/49, 60-769 Poznań, Poland, domanski@amu.edu.pl
  • Department of Mathematics, Åbo Akademi University, FIN-20500 Åbo, Finland, mlindstr@abo.fi
Bibliografia
  • [A] S. Axler, Multiplication operators on Bergman spaces, J. Reine Angew. Math. 336 (1982), 26-44.
  • [BO] B. Berndtsson and J. Ortega-Cerdà, On interpolation and sampling in Hilbert spaces of analytic functions, ibid. 464 (1995), 109-128.
  • [BBT] K. D. Bierstedt, J. Bonet and J. Taskinen, Associated weights and spaces of holomorphic functions, Studia Math. 127 (1998), 70-79.
  • [BS] K. D. Bierstedt and W. H. Summers, Biduals of weighted Banach spaces of analytic functions, J. Austral. Math. Soc. Ser. A 54 (1993), 70-79.
  • [BDL] J. Bonet, P. Domański and M. Lindström, Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions, Canad. Math. Bull. 42 (1999), 139-148.
  • [BDLT] J. Bonet, P. Domański, M. Lindström and J. Taskinen, Composition operators between weighted Banach spaces of analytic functions, J. Austral. Math. Soc. 64 (1998), 101-118.
  • [B] P. S. Bourdon, Invariant manifolds of hypercyclic vectors, Proc. Amer. Math. Soc. 118 (1993), 845-847.
  • [ChD] M. D. Choi and C. Davis, The spectral mapping theorem for joint approximative point spectrum, Bull. Amer. Math. Soc. 80 (1974), 317-321.
  • [C] J. B. Conway, A Course in Functional Analysis, Springer, Berlin, 1990.
  • [DL] P. Domański and M. Lindström, Sets of interpolation and sampling for weighted Banach spaces of holomorphic functions, preprint, 1998.
  • [G] J. B. Garnett, Bounded Analytic Functions, Academic Press, 1981.
  • [GS] G. Godefroy and J. H. Shapiro, Operators with dense, invariant, cyclic vector manifold, J. Funct. Anal. 98 (1991), 229-269.
  • [Go] P. Gorkin, Functions not vanishing on trivial Gleason parts of Douglas algebras, Proc. Amer. Math. Soc. 104 (1988), 1086-1090.
  • [H] K. Hoffman, Bounded analytic functions and Gleason parts, Ann. of Math. 86 (1967), 74-111.
  • [KL] A. Kerr-Lawson, Some lemmas on interpolating Blaschke products and a correction, Canad. J. Math. 21 (1969), 531-534.
  • [L1] W. Lusky, On the structure of $Hv_ 0(D)$ and $hv_ 0(D)$, Math. Nachr. 159 (1992), 279-289.
  • [L2] W. Lusky, On weighted spaces of harmonic and holomorphic functions, J. London Math. Soc. (2) 51 (1995), 309-320.
  • [MS] G. McDonald and C. Sundberg, Toeplitz operators on the disc, Indiana Univ. Math. J. 28 (1979), 595-611.
  • [N] A. Nicolau, Finite products of interpolating Blaschke products, J. London Math. Soc. 50 (1994), 520-531.
  • [RS] L. A. Rubel and A. L. Shields, The second duals of certain spaces of analytic functions, J. Austral. Math. Soc. 11 (1970), 276-280.
  • [R1] W. Rudin, Functional Analysis, McGraw-Hill, 1974.
  • [R2] W. Rudin, Real and Complex Analysis, McGraw-Hill, 1974.
  • [S] K. Seip, Beurling type density theorems in the unit disk, Invent. Math. 113 (1993), 21-39.
  • [S1] K. Seip, On Korenblum's density condition for the zero sequences of $A^ -α$, J. Anal. Math. 67 (1995), 307-322.
  • [S2] K. Seip, Developments from nonharmonic Fourier series, in: Proc. ICM 1998, Vol. II, 713-722.
  • [Sh] J. O. Shapiro, Composition Operators and Classical Function Theory, Springer, 1993.
  • [SW] A. L. Shields and D. L. Williams, Bounded projections and the growth of harmonic conjugates in the disk, Michigan Math. J. 29 (1982), 3-25.
  • [SZ] Z. Słodkowski and W. Żelazko, On joint spectra of commuting families of operators, Studia Math. 50 (1974), 127-148.
  • [V] D. Vukotić, Pointwise multiplication operators between Bergman spaces on simply connected domains, Indiana Univ. Math. J., to appear.
  • [Z] W. Żelazko, An axiomatic approach to joint spectra I, Studia Math. 64 (1979), 249-261.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv137i2p177bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.