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On derivations and crossed homomorphisms

100%
Losert V.
Banach Center Publications
|
2010
|
tom 91
|
nr 1
199-217
EN
We discuss some results about derivations and crossed homomorphisms arising in the context of locally compact groups and their group algebras, in particular, L¹(G), the von Neumann algebra VN(G) and actions of G on related algebras. We answer a question of Dales, Ghahramani, Grønbæk, showing that L¹(G) is always permanently weakly amenable. Then we show that for some classes of groups (e.g. IN-groups) the homology of L¹(G) with coefficients in VN(G) is trivial. But this is no longer true, in general, if VN(G) is replaced by other von Neumann algebras, like ℬ(L²(G)). Finally, as an example of a non-discrete, non-amenable group, we investigate the case of G = SL(2,ℝ) where the situation is rather different.
2
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On Hartman almost periodic functions

63%
Cohen G., Losert V.
Studia Mathematica
|
2006
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tom 173
|
nr 1
81-101
EN
We consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in $ℝ^{d}$ or $ℤ^{d}$. We consider the behavior of their Fourier-Bohr coefficients and their spectrum, depending on the particular averaging sequence, and we demonstrate this dependence by several examples. Extensions to compactly generated, locally compact, abelian groups are considered. We define generalized Marcinkiewicz spaces based upon arbitrary measure spaces and general averaging sequences of subsets. We extend results of Urbanik to locally compact abelian groups.
3
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Uniqueness of Cartesian Products of Compact Convex Sets

51%
Lipecki Z., Losert V., Spurný J.
Bulletin of the Polish Academy of Sciences. Mathematics
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2011
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tom 59
|
nr 2
175-183
EN
Let $X_i$, i∈ I, and $Y_j$, j∈ J, be compact convex sets whose sets of extreme points are affinely independent and let φ be an affine homeomorphism of $∏_{i∈ I} X_i$ onto $∏_{j∈ J} Y_j$. We show that there exists a bijection b: I → J such that φ is the product of affine homeomorphisms of $X_i$ onto $Y_{b(i)}$, i∈ I.
4
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w*-closed subalgebras of $L^∞(G)$

32%
Losert V.
Colloquium Mathematicum
|
1982
|
tom 46
|
nr 2
279-281
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