[Settfa] Tuesday 19/03, Bence Horvath

[kubis at math.cas.cz]

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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 < 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.)

 For more information see the seminar web page at 
 https://calendar.math.cas.cz/set-theory-and-analysis-actual .