# The SHAI property for the operators on L^p

@inproceedings{Johnson2021TheSP, title={The SHAI property for the operators on L^p}, author={W. Johnson and N. Phillips and G. Schechtman}, year={2021} }

A Banach space X has the SHAI (surjective homomorphisms are injective) property provided that for every Banach space Y , every continuous surjective algebra homomorphism from the bounded linear operators on X onto the bounded linear operators on Y is injective. The main result gives a sufficient condition for X to have the SHAI property. The condition is satisfied for Lp(0, 1) for 1 < p < ∞, spaces with symmetric bases that have finite cotype, and the Schatten p-spaces for 1 < p < ∞. 1 The main… Expand

#### References

SHOWING 1-10 OF 25 REFERENCES

When are full representations of algebras of operators on Banach spaces automatically faithful

- Mathematics
- 2018

We examine the phenomenon when surjective algebra homomorphisms between algebras of operators on Banach spaces are automatically injective. In the first part of the paper we shall show that for… Expand

An ordinal LP-index for Banach spaces, with application to complemented subspaces of LP

- Mathematics
- 1981

One of the central problems in the Banach space theory of the LP-spaces is to classify their complemented subspaces up to isomorphism (i.e., linear homeomorphism). Let us fix 1 < p < xc, p =# 2.… Expand

ON SUBSEQUENCES OF THE HAAR SYSTEM IN C ( h )

Spaces arising as spans of subsequences of the Haar system in C(A) are studied. It is shown that for any compact metric space H there is a subsequence whose span is isomorphic to C(H), yet that… Expand

Banach algebras and automatic continuity

- Mathematics
- 2000

Banach algebras combine algebraic and analytical aspects: it is the interplay of these structures that gives the subject its fascination. This volume expounds the general theory of Banach algebras,… Expand

Topics in Banach space theory

- Mathematics
- 2006

This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible… Expand

Some linear topological properties of the spaces $C_p$ of operators on Hilbert space

- Mathematics
- 1975

© Foundation Compositio Mathematica, 1975, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions… Expand

Classical Banach spaces

- Computer Science
- 1973

Springer-Verlag is reissuing a selected few of these highly successful books in a new, inexpensive sofcover edition to make them easily accessible to younger generations of students and researchers. Expand

On the subspaces of L (p > 2) spanned by sequences of independent random variables

- Israel J. Math. 8
- 1970

Examples of Lp spaces (1 < p 6= 2 < ∞)

- Israel J. Math. 22
- 1975

lczyński, The main triangle projection in matrix spaces and its applications

- Studia Math
- 1970