[Settfa] Tuesday 19/03, Bence Horvath

kubis at math.cas.cz kubis at math.cas.cz
Fri Mar 15 17:00:02 CET 2019

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Tuesday 19th March, 10:00am
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Speaker:Bence Horvath, IM CAS
Title: Surjective homomorphisms of algebras of operators on Banach spaces

Abstract

A classical result of Eidelheit asserts that if X and Y are Banach spaces then

they are isomorphic if and only if their algebras of operators B(X) and B(Y) are

isomorphic as Banach algebras, in the sense that there is a continuous bijective algebra

homomorphism \psi : B(X) \to B(Y). It is natural to ask whether for some class of

Banach spaces X this theorem can be strengthened in the following sense: If Y is a

non-zero Banach space and \psi : B(X) \to B(Y ) is a surjective algebra homomorphism,

is \psi automatically injective?

It is easy to see that for a "very nice" class Banach spaces, such as c_0 and \ell_p, where

1 ? p &lt; 1, the answer is positive. In our talk we shall present methods which allow us

to extend the range of positive examples, including \ell_1 and Hilbert spaces of arbitrary

density character. Time permittingwe present a permanence-type result too.

(See the attached pdf file for more details.)