Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
We investigate conditions under which the projective and the injective topologies coincide on the tensor product of two Köthe echelon or coechelon spaces. A major tool in the proof is the characterization of the επ-continuity of the tensor product of two diagonal operators from $l_p$ to $l_q$. Several sharp forms of this result are also included.
Kategorie tematyczne
- 46B20: Geometry and structure of normed linear spaces
- 46M05: Tensor products
- 46A32: Spaces of linear operators; topological tensor products; approximation properties
- 46A45: Sequence spaces (including K\"othe sequence spaces)
- 46B45: Banach sequence spaces
- 46B28: Spaces of operators; tensor products; approximation properties
Czasopismo
Rocznik
Tom
Numer
Strony
263-281
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-11-08
poprawiono
1994-01-31
Twórcy
autor
- Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, E-46071 Valencia, Spain, mat6jbs0@cci.upv.es
autor
- FB Mathematik, Universität Oldenburg, D-26121 Oldenburg, Germany, 53784@vmxa.hrz.uni-oldenburg.de
autor
- Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, E-46071 Valencia, Spain, mat6apm@cci.upv.es
autor
- Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109, U.S.A., msram@math.lsa.umich.edu
Bibliografia
- [1] V. Bartík, K. John and J. Korbaš, Tensor products of operators and Horn's inequality, in: Oper. Theory: Adv. Appl. 14, Birkhäuser, Basel, 1984, 39-46.
- [2] K. D. Bierstedt und R. Meise, Induktive Limiten gewichteter Räume stetiger und holomorpher Funktionen, J. Reine Angew. Math. 282 (1976), 186-220.
- [3] K. D. Bierstedt, R. Meise and W. H. Summers, A projective description of weighted inductive limits, Trans. Amer. Math. Soc. 272 (1982), 107-160.
- [4] K. D. Bierstedt, R. Meise and W. H. Summers, Köthe sets and Köthe sequence spaces, in: Functional Analysis, Holomorphy and Approximation Theory, North-Holland Math. Stud. 71, North-Holland, 1982, 27-91.
- [5] B. Carl, B. Maurey und J. Puhl, Grenzordnungen von absolut-(r, p)-summierenden Operatoren, Math. Nachr. 82 (1978), 205-218.
- [6] A. Defant, Barrelledness and nuclearity, Arch. Math. (Basel) 44 (1985), 168-170.
- [7] A. Defant and K. Floret, Topological tensor products and the approximation property of locally convex spaces, Bull Soc. Roy. Sci. Liège 58 (1989), 29-51.
- [8] A. Defant and K. Floret, Tensor Norms and Operator Ideals, North-Holland Math. Stud. 176, North-Holland, 1993.
- [9] A. Defant and V. Mascioni, Limit orders of ε-π continuous operators, Math. Nachr. 145 (1990), 337-344.
- [10] A. Defant and L. A. Moraes, On unconditional bases in spaces of holomorphic functions in infinite dimensions, Arch. Math. (Basel) 56 (1991), 163-173.
- [11] S. Dineen and R. M. Timoney, Absolute bases, tensor products and a theorem of Bohr, Studia Math. 94 (1989), 227-234.
- [12] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
- [13] H. Jarchow, Locally Convex Spaces, Teubner, 1981.
- [14] H. Jarchow and K. John, On the equality of injective and projective tensor products, Czechoslovak Math. J. 38 (1988), 464-472.
- [15] H. Jarchow and K. John, Bilinear forms and nuclearity, preprint, 1992.
- [16] K. John, Counterexample to a conjecture of Grothendieck, Math. Ann. 265 (1983), 169-179.
- [17] K. John, On the compact non-nuclear operator problem, ibid. 287 (1990), 509-514.
- [18] G. Köthe, Topological Vector Spaces I, II, Springer, 1969, 1979.
- [19] P. Pérez Carreras and J. Bonet, Barrelled Locally Convex Spaces, North-Holland Math. Stud. 131, North-Holland, 1987.
- [20] A. Pietsch, Nuclear Locally Convex Spaces, Springer, 1972.
- [21] A. Pietsch, Operator Ideals, Deutscher Verlag Wiss., 1978.
- [22] A. Pietsch, Eigenvalues and s-Numbers, Cambridge University Press, 1987.
- [23] G. Pisier, Counterexamples to a conjecture of Grothendieck, Acta Math. 151 (1983), 180-208.
- [24] G. Pisier, Factorization of Linear Operators and Geometry of Banach Spaces, CBMS Regional Conf. Ser. in Math. 60, Amer. Math. Soc., 1986.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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