Abstract In this paper, we give a new geometric condition in terms of measured asymptotic expanders to ensure rigidity Roe algebras. Consequently, obtain the for all bounded geometry spaces that coarsely embed into some $L^p$-space $p\in [1,\infty )$. Moreover, also verify box constructed by Arzhantseva–Tessera and Delabie–Khukhro even though they do not any $L^p$-space. The key step our proof ...

Let  and  be Banach algebras, ,  and . We define an -product on  which is a strongly splitting extension of  by . We show that these products form a large class of Banach algebras which contains all module extensions and triangular Banach algebras. Then we consider spectrum, Arens regularity, amenability and weak amenability of these products.

Ocneanu noted that the data for what is now known as a Turaev-Viro type TQFT is supplied by a subfactor N of nite index and depth of a II1 factor M . One takes all the irreducible bimodules arising in the decomposition of the tensor powers, in the sense of Connes ([3]), of the Hilbert space L(M) viewed as an N−N bimodule, or, in Connes' terminology, a correspondence. (We will use the term corre...

The efficiency–accuracy trade-off of approximate computing spans a diverse array of techniques at both the hardware and software levels. While this diversity is key to the success of approximation research, it also entails considerable complexity in developing and validating new approximation techniques. Researchers must relate their ideas to a vast body of work on approximate computing and inv...

In this paper, we introduce a weak form of amenability on topological semigroups that call $$\varphi $$ -amenability, where is character semigroup. Some basic properties new notion are obtained and by giving some examples, show definition weaker than the semigroups. As noticeable result, for semigroup S, it shown if S -amenable, then amenable. Moreover, -ergodicity introduced proved under condi...

a definition of two jointly asymptotically nonexpansive mappings s and t on uniformly convex banach space e is studied to approximate common fixed points of two such mappings through weak and strong convergence of an ishikawa type iteration scheme generated by s and t on a bounded closed and convex subset of e. as a consequence of the notion of two jointly asymptotically nonexpansive maps, we c...

We give a brief survey of many of the high-lights of our present understanding of the young subject of quantum metric spaces, and of quantum Gromov-Hausdorff distance between them. We include examples. My interest in developing the theory of compact quantum metric spaces was stimulated by certain statements in the high-energy physics and string-theory literature, concerning non-commutative spac...