PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1995 | 115 | 3 | 251-259
Tytuł artykułu

Compressible operators and the continuity of homomorphisms from algebras of operators

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The notion of a compressible operator on a Banach space, E, derives from automatic continuity arguments. It is related to the notion of a cartesian Banach space. The compressible operators on E form an ideal in ℬ(E) and the automatic continuity proofs depend on showing that this ideal is large. In particular, it is shown that each weakly compact operator on the James' space, J, is compressible, whence it follows that all homomorphisms from ℬ(J) are continuous.
Słowa kluczowe
Twórcy
autor
  • Department of Mathematics, The University of Newcastle, University Drive, Callaghan, Newcastle, N.S.W. 2308, Australia, george@frey.newcastle.edu.au
Bibliografia
  • [Da] H. G. Dales, Banach Algebras and Automatic Continuity, Oxford Univ. Press, in preparation.
  • [D,L&W] H. G. Dales, R. J. Loy and G. A. Willis, Homomorphisms and derivations from ℬ(E), J. Funct. Anal., to appear.
  • [Go] W. T. Gowers, A solution to the Schroeder-Bernstein problem for Banach spaces, preprint.
  • [GM1] W. T. Gowers and B. Maurey, The unconditional basic sequence problem, J. Amer. Math. Soc. 6 (1993), 851-874.
  • [GM2] W. T. Gowers and B. Maurey, Banach spaces with small spaces of operators, preprint.
  • [Ja] R. C. James, A non-reflexive Banach space isometric with its second conjugate space, Proc. Nat. Acad. Sci. U.S.A. 37 (1950), 174-177.
  • [BJo] B. E. Johnson, Continuity of homomorphisms from algebras of operators, J. London Math. Soc. 42 (1967), 537-541.
  • [WJo1] W. B. Johnson, Factoring compact operators, Israel J. Math. 9 (1971), 337-345.
  • [WJo2] W. B. Johnson, A complementary universal conjugate Banach space and its relation to the approximation problem, ibid. 13 (1972), 301-310.
  • [L&W] R. J. Loy and G. A. Willis, Continuity of derivations on ℬ(E) for certain Banach spaces E, J. London Math. Soc. (2) 40 (1989), 327-346.
  • [Og] C. Ogden, Homomorphisms from $B(C_ω_η)$, J. London Math. Soc., to appear.
  • [Re] C. J. Read, Discontinuous derivations on the algebra of bounded operators on a Banach space, ibid. (2) 40 (1989), 305-326.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv115i3p251bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.