Displaying similar documents to “Supersets for the spectrum of elements in extended Banach algebras.”

The basic sequence problem

N. Kalton (1995)

Studia Mathematica

Similarity:

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

On generalized derivations in Banach algebras

Nadia Boudi, Said Ouchrif (2009)

Studia Mathematica

Similarity:

We study generalized derivations G defined on a complex Banach algebra A such that the spectrum σ(Gx) is finite for all x ∈ A. In particular, we show that if A is unital and semisimple, then G is inner and implemented by elements of the socle of A.

Bounded elements and spectrum in Banach quasi *-algebras

Camillo Trapani (2006)

Studia Mathematica

Similarity:

A normal Banach quasi *-algebra (,) has a distinguished Banach *-algebra b consisting of bounded elements of . The latter *-algebra is shown to coincide with the set of elements of having finite spectral radius. If the family () of bounded invariant positive sesquilinear forms on contains sufficiently many elements then the Banach *-algebra of bounded elements can be characterized via a C*-seminorm defined by the elements of ().

Linear maps preserving quasi-commutativity

Heydar Radjavi, Peter Šemrl (2008)

Studia Mathematica

Similarity:

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.

Wiener amalgam spaces with respect to quasi-Banach spaces

Holger Rauhut (2007)

Colloquium Mathematicae

Similarity:

We generalize the theory of Wiener amalgam spaces on locally compact groups to quasi-Banach spaces. As a main result we provide convolution relations for such spaces. Also we weaken the technical assumption that the global component is invariant under right translations, which is new even for the classical Banach space case. To illustrate our theory we discuss in detail an example on the ax+b group.

Bayoumi quasi-differential is not different from Fréchet-differential

Fernando Albiac, José Ansorena (2012)

Open Mathematics

Similarity:

Unlike for Banach spaces, the differentiability of functions between infinite-dimensional nonlocally convex spaces has not yet been properly studied or understood. In a paper published in this Journal in 2006, Bayoumi claimed to have discovered a new notion of derivative that was more suitable for all F-spaces including the locally convex ones with a wider potential in analysis and applied mathematics than the Fréchet derivative. The aim of this short note is to dispel this misconception,...