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: 5

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

Banach algebras with unique uniform norm II

100%
Bhatt S., Dedania H.
Studia Mathematica
|
2001
|
tom 147
|
nr 3
211-235
EN
Semisimple commutative Banach algebras 𝓐 admitting exactly one uniform norm (not necessarily complete) are investigated. 𝓐 has this Unique Uniform Norm Property iff the completion U(𝓐) of 𝓐 in the spectral radius r(·) has UUNP and, for any non-zero spectral synthesis ideal ℐ of U(𝓐), ℐ ∩ 𝓐 is non-zero. 𝓐 is regular iff U(𝓐) is regular and, for any spectral synthesis ideal ℐ of 𝓐, 𝓐/ℐ has UUNP iff U(𝓐) is regular and for any spectral synthesis ideal ℐ of U(𝓐), ℐ = k(h(𝓐 ∩ ℐ)) (hulls and kernels in U(𝓐)). 𝓐 has UUNP and the Shilov boundary coincides with the Gelfand space iff 𝓐 is weakly regular in the sense that, given a proper, closed subset F of the Gelfand space, there exists a non-zero x in 𝓐 having its Gelfand transform vanishing on F. Several classes of Banach algebras that are weakly regular but not regular, as well as those that are not weakly regular but have UUNP are exhibited. The UUNP is investigated for quotients, tensor products, and multiplier algebras. The property UUNP compares with the unique C*-norm property on (not necessarily commutative) Banach *-algebras. The results are applied to multivariate holomorphic function algebras as well as to the measure algebra of a locally compact abelian group G. For a continuous weight ω on G, the Beurling algebra L¹(G,ω) (assumed semisimple) has UUNP iff it is regular.
2
Content available remote

Weighted measure algebras and uniform norms

100%
Bhatt S., Dedania H.
Studia Mathematica
|
2006
|
tom 177
|
nr 2
133-139
EN
Let ω be a weight on an LCA group G. Let M(G,ω) consist of the Radon measures μ on G such that ωμ is a regular complex Borel measure on G. It is proved that: (i) M(G,ω) is regular iff M(G,ω) has unique uniform norm property (UUNP) iff L¹(G,ω) has UUNP and G is discrete; (ii) M(G,ω) has a minimum uniform norm iff L¹(G,ω) has UUNP; (iii) M₀₀(G,ω) is regular iff M₀₀(G,ω) has UUNP iff L¹(G,ω) has UUNP, where M₀₀(G,ω) := {μ ∈ M(G,ω) : μ̂ = 0 on Δ(M(G,ω))∖Δ(L¹(G,ω))}.
3
Content available remote

Beurling algebras and uniform norms

100%
Bhatt S., Dedania H.
Studia Mathematica
|
2004
|
tom 160
|
nr 2
179-183
EN
Given a locally compact abelian group G with a measurable weight ω, it is shown that the Beurling algebra L¹(G,ω) admits either exactly one uniform norm or infinitely many uniform norms, and that L¹(G,ω) admits exactly one uniform norm iff it admits a minimum uniform norm.
4
Content available remote

Beurling algebra analogues of theorems of Wiener-Lévy-Żelazko and Żelazko

81%
Bhatt S., Dabhi P., Dedania H.
Studia Mathematica
|
2009
|
tom 195
|
nr 3
219-225
EN
Let 0 < p ≤ 1, let ω: ℤ → [1,∞) be a weight on ℤ and let f be a nowhere vanishing continuous function on the unit circle Γ whose Fourier series satisfies $∑_{n∈ℤ} |f̂(n)|^{p}ω(n) < ∞$. Then there exists a weight ν on ℤ such that $∑_{n∈ℤ} |\widehat{(1/f)}(n)|^{p} ν(n) < ∞$. Further, ν is non-constant if and only if ω is non-constant; and ν = ω if ω is non-quasianalytic. This includes the classical Wiener theorem (p = 1, ω = 1), Domar theorem (p = 1, ω is non-quasianalytic), Żelazko theorem (ω = 1) and a recent result of Bhatt and Dedania (p = 1). An analogue of the Lévy theorem at the present level of generality is also developed. Given a locally compact group G with a continuous weight ω and 0 < p < 1, the locally bounded space $L^{p}(G,ω)$ is closed under convolution if and only if G is discrete if and only if G admits an atom. This generalizes and refines another result of Żelazko.
5
Content available remote

Spectral well-behaved *-representations

81%
Bhatt S., Fragoulopoulou M., Inoue A.
Banach Center Publications
|
2005
|
tom 67
|
nr 1
123-131
EN
In this brief account we present the way of obtaining unbounded *-representations in terms of the so-called "unbounded" C*-seminorms. Among such *-representations we pick up a special class with "good behaviour" and characterize them through some properties of the Pták function.
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.