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: 7

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

The GRS-condition and symmetry of weighted L¹-algebras

100%
Leinert M.
Banach Center Publications
|
2006
|
tom 73
|
nr 1
309-312
2
Content available remote

Isomorphisms of AC(σ) spaces

64%
Doust I., Leinert M.
Studia Mathematica
|
2015
|
tom 228
|
nr 1
7-31
EN
Analogues of the classical Banach-Stone theorem for spaces of continuous functions are studied in the context of the spaces of absolutely continuous functions introduced by Ashton and Doust. We show that if AC(σ₁) is algebra isomorphic to AC(σ₂) then σ₁ is homeomorphic to σ₂. The converse however is false. In a positive direction we show that the converse implication does hold if the sets σ₁ and σ₂ are confined to a restricted collection of compact sets, such as the set of all simple polygons.
3
Content available remote

On a translation property of positive definite functions

64%
Omlor L., Leinert M.
Banach Center Publications
|
2010
|
tom 89
|
nr 1
237-240
EN
If G is a locally compact group with a compact invariant neighbourhood of the identity e, the following property (*) holds: For every continuous positive definite function h≥ 0 with compact support there is a constant $C_{h} > 0$ such that $∫ L_{x}h·g ≤ C_{h}∫ hg$ for every continuous positive definite g≥0, where $L_{x}$ is left translation by x. In [L], property (*) was stated, but the above inequality was proved for special h only. That "for one h" implies "for all h" seemed obvious, but turned out not to be obvious at all. We fill this gap by means of a new structure theorem for IN-groups. For p ∈ ℕ even, property (*) easily implies the following property (*)ₚ: For every relatively compact invariant neighbourhood U of e, there is a constant $C_{U} > 0$ such that $||χ_{xU}·g||ₚ ≤ C_{U}||χ_{U}·g||ₚ$ for every continuous positive definite function g. For all other p ∈ (1,∞), property (*)ₚ fails (see [L]). In the special case of the unit circle, the || ||ₚ-norm results are essentially due to N. Wiener, S. Wainger, and H. S. Shapiro. For compact abelian groups they are due to M. Rains, and for locally compact abelian groups to J. Fournier.
4
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Separable translation-invariant subspaces of M(G) and other dual spaces on locally compact groups

51%
Graham C. C., To-Ming Lau A., Leinert M.
Colloquium Mathematicum
|
1988
|
tom 55
|
nr 1
131-145
5
Content available remote

On spectrality of the algebra of convolution dominated operators

51%
Fendle G., Gröchenig K., Leinert M.
Banach Center Publications
|
2007
|
tom 78
|
nr 1
145-149
EN
If G is a discrete group, the algebra CD(G) of convolution dominated operators on l²(G) (see Definition 1 below) is canonically isomorphic to a twisted L¹-algebra $l¹(G,l^{∞}(G),T)$. For amenable and rigidly symmetric G we use this to show that any element of this algebra is invertible in the algebra itself if and only if it is invertible as a bounded operator on l²(G), i.e. CD(G) is spectral in the algebra of all bounded operators. For G commutative, this result is known (see [1], [6]), for G noncommutative discrete it appears to be new. This note is about work in progress. Complete details and more will be given in [3].
6
Content available remote

Convolution-dominated integral operators

51%
Fendler G., Gröchenig K., Leinert M.
Banach Center Publications
|
2010
|
tom 89
|
nr 1
121-127
EN
For a locally compact group G we consider the algebra CD(G) of convolution-dominated operators on L²(G), where an operator A: L²(G) → L²(G) is called convolution-dominated if there exists a ∈ L¹(G) such that for all f ∈ L²(G) |Af(x)| ≤ a⋆|f|(x), for almost all x ∈ G. (1) The case of discrete groups was treated in previous publications \cite{fgl08a, fgl08}. For non-discrete groups we investigate a subalgebra of regular convolution-dominated operators generated by product convolution operators, where the products are restricted to those given by multiplication with left uniformly continuous functions. This algebra, $CD_{reg}(G)$, is canonically isomorphic to a twisted L¹-algebra. For amenable G that is rigidly symmetric as a discrete group we show the following result: An element of $CD_{reg}(G)$ is invertible in $CD_{reg}(G)$ if and only if it is invertible as a bounded operator on L²(G). This report is about work in progress. Complete details and further results will be given in a paper still in preparation.
7
Content available remote

Faltungsoperatoren auf gewissen diskreten Gruppen

32%
Leinert M.
Studia Mathematica
|
1974-1975
|
tom 52
|
nr 2
149-158
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.