Isomorphisms of algebras of convolution operators
نویسندگان
چکیده
For $p,q\in [1,\infty)$, we study the isomorphism problem for $p$- and $q$-convolution algebras associated to locally compact groups. While it is well known that not every group can be recovered from its von Neumann algebra, show this case $\mathrm{CV}_p(G)$ of $p$-convolvers $\mathrm{PM}_p(G)$ $p$-pseudomeasures, $p\neq 2$. More generally, if isometrically isomorphic $\mathrm{CV}_q(H)$, with $p,q\neq 2$, then $G$ must $H$ $p$ $q$ are either equal or conjugate. This implies there no $L^p$-version Connes' uniqueness hyperfinite II$_1$-factor. Similar results apply algebra $\mathrm{PF}_p(G)$ $p$-pseudofunctions, generalizing a classical result Wendel. We also other $L^p$-rigidity groups easily extended using our main theorem. Our answer questions originally formulated in work Herz 70's. Moreover, methods reveal new information about Banach question. As non-trivial application, verify reflexivity conjecture all lying between $\mathrm{CV}_p(G)$: any such reflexive amenable, finite.
منابع مشابه
Isomorphisms between Algebras of Semiclassical Pseudodifferential Operators
Following the work of Duistermaat-Singer [DS] on isomorphisms of algebras of global pseudodifferential operators, we classify isomorphisms of algebras of microlocally defined semiclassical pseudodifferential operators. Specifically, we show that any such isomorphism is given by conjugation by A = BF , where B is a microlocally elliptic semiclassical pseudodifferential operator, and F is a micro...
متن کاملamenability of banach algebras
chapters 1 and 2 establish the basic theory of amenability of topological groups and amenability of banach algebras. also we prove that. if g is a topological group, then r (wluc (g)) (resp. r (luc (g))) if and only if there exists a mean m on wluc (g) (resp. luc (g)) such that for every wluc (g) (resp. every luc (g)) and every element d of a dense subset d od g, m (r)m (f) holds. chapter 3 inv...
15 صفحه اولsome properties of fuzzy hilbert spaces and norm of operators
in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...
15 صفحه اولWeighted Convolution Measure Algebras Characterized by Convolution Algebras
The weighted semigroup algebra Mb (S, w) is studied via its identification with Mb (S) together with a weighted algebra product *w so that (Mb (S, w), *) is isometrically isomorphic to (Mb (S), *w). This identification enables us to study the relation between regularity and amenability of Mb (S, w) and Mb (S), and improve some old results from discrete to general case.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales Scientifiques De L Ecole Normale Superieure
سال: 2022
ISSN: ['0012-9593', '1873-2151']
DOI: https://doi.org/10.24033/asens.2520