Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 4

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

Unital strongly harmonic commutative Banach algebras

100%
Bračič J.
Studia Mathematica
|
2002
|
tom 149
|
nr 3
253-266
EN
A unital commutative Banach algebra 𝓐 is spectrally separable if for any two distinct non-zero multiplicative linear functionals φ and ψ on it there exist a and b in 𝓐 such that ab = 0 and φ(a)ψ(b) ≠ 0. Spectrally separable algebras are a special subclass of strongly harmonic algebras. We prove that a unital commutative Banach algebra 𝓐 is spectrally separable if there are enough elements in 𝓐 such that the corresponding multiplication operators on 𝓐 have the decomposition property (δ). On the other hand, if 𝓐 is spectrally separable, then for each a ∈ 𝓐 and each Banach left 𝓐 -module 𝒳 the corresponding multiplication operator $L_{a}$ on 𝒳 is super-decomposable. These two statements improve an earlier result of Baskakov.
2
Content available remote

Local spectrum and local spectral radius of an operator at a fixed vector

63%
Bračič J., Müller V.
Studia Mathematica
|
2009
|
tom 194
|
nr 2
155-162
EN
Let 𝒳 be a complex Banach space and e ∈ 𝒳 a nonzero vector. Then the set of all operators T ∈ ℒ(𝒳) with $σ_{T}(e) = σ_δ(T)$, respectively $r_{T}(e) = r(T)$, is residual. This is an analogy to the well known result for a fixed operator and variable vector. The results are then used to characterize linear mappings preserving the local spectrum (or local spectral radius) at a fixed vector e.
3
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Maximal abelian subalgebras of \(B(\mathcal{X})\)

63%
Bračič J., Kuzma B.
Commentationes Mathematicae
|
2008
|
tom 48
|
nr 1
EN
Let \(\mathcal{X}\) be an infinite dimensional complex Banach space and \(B(\mathcal{X})\) be the Banach algebra of all bounded linear operators on \(\mathcal{X}\). Żelazko [1] posed the following question: Is it possible that some maximal abelian subalgebra of \(B(\mathcal{X})\) is finite dimensional? Interestingly, he was able to show that there does exist an infinite dimensional closed subalgebra of \(B(\mathcal{X})\) with all but one maximal abelian subalgebras of dimension two. The aim of this note is to give a negative answer to the original question and prove that there does not exist a finite dimensional maximal commutative subalgebra of \(B(\mathcal{X})\) if \(\text{dim} X = \infty\).
4
Content available remote

Non-hyperreflexive reflexive spaces of operators

51%
Bessonov R., Bračič J., Zajac M.
Studia Mathematica
|
2011
|
tom 202
|
nr 1
65-80
EN
We study operators whose commutant is reflexive but not hyperreflexive. We construct a C₀ contraction and a Jordan block operator $S_{B}$ associated with a Blaschke product B which have the above mentioned property. A sufficient condition for hyperreflexivity of $S_{B}$ is given. Some other results related to hyperreflexivity of spaces of operators that could be interesting in themselves are proved.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.