Compressible operators and the continuity of homomorphisms from algebras of operators

• Autorzy: G. A. Willis
• 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.

Kategorie tematyczne

• 47L10: Algebras of operators on Banach spaces and other topological linear spaces
• 46H40: Automatic continuity
• 46B03: Isomorphic theory (including renorming) of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995
• Tom: 115
• Numer: 3
• Strony: 251-259

Daty

wydano

1995

otrzymano

1994-08-24

poprawiono

1995-03-01

Twórcy

autor

G. A. Willis

• Department of Mathematics, The University of Newcastle, University Drive, Callaghan, Newcastle, N.S.W. 2308, Australia

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.