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In this paper, we study the generalized differentiability of the metric projection operator onto the positive cone in Hilbert spaces. We first establish the formula for exactly computing the regular coderivative and the Mordukhovich…
In this paper we consider A-Fredholm and semi-A-Fredholm operators on Hilbert C*-modules over a W*-algebra A defined in [3],[10]. Using the assumption that A is a W*-algebra (and not an arbitrary C*-algebra), we obtain several results such…
The objectives of this research work which is intimately related to pattern discovery and management are threefold: (i) handle the problem of pattern manipulation by defining operations on patterns, (ii) study the problem of enriching and…
We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…
In a previous paper we showed how the main theorems characterizing operator algebras and operator modules, fit neatly into the framework of the `noncommutative Shilov boundary', and more particularly via the left multiplier operator algebra…
We introduce a generalization of the notion of operad that we call a contractad, whose set of operations is indexed by connected graphs and whose composition rules are numbered by contractions of connected subgraphs. We show that many…
Let $A$ be a unital operator algebra. Let us assume that every {\it bounded\/} unital homomorphism $u\colon \ A\to B(H)$ is similar to a {\it contractive\/} one. Let $\text{\rm Sim}(u) = \inf\{\|S\|\, \|S^{-1}\|\}$ where the infimum runs…
We discuss some basic problems and conjectures in a program to construct general orbifold conformal field theories using the representation theory of vertex operator algebras. We first review a program to construct conformal field theories.…
Hilbert C*-modules are the analogues of Hilbert spaces where a C*-algebra plays the role of the scalar field. With the advent of Kasparov's celebrated KK-theory they became a standard tool in the theory of operator algebras. While the…
This text, based on the author's Bachelor's thesis, introduces the theory of Algebraic Operads, a mathematical formalism that provides a unifying framework for modern algebra. We demonstrate how the fundamental theories of associative,…
In the 1970s Alain Connes identified the appropriate notion of amenabilty for von Neumann algebras, and used it to obtain a deep internal finite dimensional approximation structure for these algebras. This structure is exactly what is…
We establish several operator versions of the classical Aczel inequality. One of operator versions deals with the weighted operator geometric mean and another is related to the positive sesquilinear forms. Some applications including the…
In this paper, we prove some common coupled fixed point theorems for mappings satisfying different contractive conditions in the context of complete $C^*$-algebra-valued metric spaces. Moreover, the paper provides an application to prove…
The order relation on the set of completely n-positive linear maps from a pro-C*-algebra A to L(H), the C*-algebra of bounded linear operators on a Hilbert space H, is characterized in terms of the representation associated with each…
Frames on Hilbert C*-modules have been defined for unital C*-algebras by Frank and Larson and operator valued frames on a Hilbert space have been studied in arXiv.0707.3272v1.[math.FA]. Goal of the present paper is to introduce operator…
The Operator axioms have produced new real numbers with new operators. New operators naturally produce new equations and thus extend the traditional mathematical models which are selected to describe various scientific rules. So new…
A C*-algebra formulation of Quantum Mechanics is derived from purely operational axioms in which the primary role is played by the "transformations" that the system undergoes in the course of an "experiment". The notion of the {\em adjoint}…
The purpose of this short note is to clarify and present a general version of an interesting observation by Piani and Mora (Physic. Rev. A 75, 012305 (2007)), linking complete positivity of linear maps on matrix algebras to decomposability…
As a pioneering work we construct explicit real algebraic functions which may have both compact and non-compact preimages. The author has obtained explicit real algebraic functions with preimages satisfying some nice conditions. More…
We characterize projections among positive norm-one elements in unital C$^*$-algebras in pure geometric terms determined by the norm of the underlying Banach space. Concretely, let $A$ be a C$^*$-algebra (or a JB$^*$-algebra) whose positive…