We consider Schatten ́s equation in connection with a Banach algebra and Banach modules. From this connection we infer a new proof of the fact that the second action of a bounded derivation is also a bounded derivation.

A completely bounded bilinear operator φ: M×M → M on a von Neumann algebra M is said to have a factorization in M if there exist completely bounded linear operators ψj , θj : M → M such that

In this paper, we introduce an algebra of singular integral operators containing Bessel potentials of positive order, and show that the corresponding unital Banach algebra is an inverseclosed Banach subalgebra of B(Lw), the Banach algebra of all bounded operators on the weighted space Lw, for all 1 ≤ q < ∞ and Muckenhoupt Aq-weights w. Mathematics Subject Classification (2000) 47L80, 42B20, 45P...

We show that the matricial norms of a non-unital operator algebra determine those of the algebra obtained by adjoining a unit to it. As applications , we classify two-dimensional unital operator algebras and show that the algebra of bounded holomorphic functions on a strongly pseudoconvex domain has a contractive representation that is not completely contractive.

Comparing the bounded derived categories of an algebra and endomorphism a given support {\tau}-tilting module, we find relation between dimensions module.

Let A be a C∗-algebra, and let X be a Banach A-bimodule. B. E. Johnson showed that local derivations from A into X are derivations. We extend this concept of locality to the higher cohomology of a C ∗-algebra and show that, for every n ∈ N, bounded local n-cocycles from A into X are n-cocycles. The study of the local properties of Hochschild cohomology of a Banach algebra was initiated by intro...

Although derivations from Banach algebras to particular coefficient modules have been much studied, interest has usually focused on the existence or otherwise of non-trivial bounded derivations, rather than their characterisation. Even in the special case of derivations from a commutative Banach algebra to its dual (as in [2] or [5] for example), there are comparatively few examples where the s...

We consider two versions of the uniform Roe algebra for uniformly discrete spaces without bounded geometry and discuss some their properties.

We introduce a notion of covering dimension for Cuntz semigroups C⁎-algebras. This is always bounded by the nuclear C⁎-algebra, and subhomogeneous C⁎-algebras both dimensions agree. Z-stable have at most one. Further, semigroup simple, C⁎-algebra zero-dimensional if only has real rank zero or stably projectionless.

An important problem in analytic and geometric combinatorics is estimating the number of lattice points in a compact convex set in a Euclidean space. Such estimates have numerous applications throughout mathematics. In this note, we exhibit applications of a particular estimate of this sort to several counting problems in number theory: counting integral points and units of bounded height over ...