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Displaying similar documents to “On certain quasi-complemented and complemented Banach algebras.”

Linear maps preserving quasi-commutativity

Heydar Radjavi, Peter Šemrl (2008)

Studia Mathematica

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Let X and Y be Banach spaces and ℬ(X) and ℬ(Y) the algebras of all bounded linear operators on X and Y, respectively. We say that A,B ∈ ℬ(X) quasi-commute if there exists a nonzero scalar ω such that AB = ωBA. We characterize bijective linear maps ϕ : ℬ(X) → ℬ(Y) preserving quasi-commutativity. In fact, such a characterization can be proved for much more general algebras. In the finite-dimensional case the same result can be obtained without the bijectivity assumption.

The basic sequence problem

N. Kalton (1995)

Studia Mathematica

Similarity:

We construct a quasi-Banach space X which contains no basic sequence.