# Compressible operators and the continuity of homomorphisms from algebras of operators

Studia Mathematica (1995)

- Volume: 115, Issue: 3, page 251-259
- ISSN: 0039-3223

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topWillis, G.. "Compressible operators and the continuity of homomorphisms from algebras of operators." Studia Mathematica 115.3 (1995): 251-259. <http://eudml.org/doc/216211>.

@article{Willis1995,

abstract = {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.},

author = {Willis, G.},

journal = {Studia Mathematica},

keywords = {compressible operator on a Banach space; automatic continuity; James' space},

language = {eng},

number = {3},

pages = {251-259},

title = {Compressible operators and the continuity of homomorphisms from algebras of operators},

url = {http://eudml.org/doc/216211},

volume = {115},

year = {1995},

}

TY - JOUR

AU - Willis, G.

TI - Compressible operators and the continuity of homomorphisms from algebras of operators

JO - Studia Mathematica

PY - 1995

VL - 115

IS - 3

SP - 251

EP - 259

AB - 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.

LA - eng

KW - compressible operator on a Banach space; automatic continuity; James' space

UR - http://eudml.org/doc/216211

ER -

## References

top- [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. Zbl0815.46063
- [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. Zbl0827.46008
- [GM2] W. T. Gowers and B. Maurey, Banach spaces with small spaces of operators, preprint. Zbl0876.46006
- [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. Zbl0152.32805
- [WJo1] W. B. Johnson, Factoring compact operators, Israel J. Math. 9 (1971), 337-345. Zbl0236.47045
- [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. Zbl0651.47035
- [Og] C. Ogden, Homomorphisms from $B\left({C}_{\omega}\eta \right)$, 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.

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