Related papers: Real operator spaces and operator algebras
A new simple geometrical interpretation of complex numbers is presented. It differs from their usual interpretation as points in the complex plane. From the new point of view the complex numbers are rather operations on vectors than points.…
We are used to thinking of an operator acting once, twice, and so on. However, an operator acting integer times can be consistently analytic continued to an operator acting complex times. Applications: (s,r) diagrams and an extension of…
Operads are algebraic devices offering a formalization of the concept of operations with several inputs and one output. Such operations can be naturally composed to form bigger and more complex ones. Coming historically from algebraic…
Extending the notion of parallelism we introduce the concept of approximate parallelism in normed spaces and then substantially restrict ourselves to the setting of Hilbert space operators endowed with the operator norm. We present several…
The TTE approach to Computable Analysis is the study of so-called representations (encodings for continuous objects such as reals, functions, and sets) with respect to the notions of computability they induce. A rich variety of such…
We give an overview of certain aspects of tractability analysis of multivariate problems. This paper is not intended to give a complete account of the subject, but provides an insight into how the theory works for particular types of…
Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, $C$-selfadjoint…
We consider an integral operator $\mathcal{I}$, special instances of which was studied in various contexts. Using an appropriate transformation we write this operator in terms of weighted composition operators. Then, we provide a…
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the…
We show that the main problem left open in Wenzel: "Real and complex operator ideals" (wenzelopidls.latex), can be solved using the Banach spaces $Z_\alpha$ recently constructed by Kalton: "An elementary example of a Banach space not…
Quantum field theory unifies concepts from quantum theory and from special relativity. Its mathematically rigorous description is quite intricate and is only partially understood; this is particularly true for the construction of operators…
We recall the notion of a differential operator over a smooth map (in linear and non-linear settings) and consider its versions such as formal $\hbar$-differential operators over a map. We study constructions and examples of such operators,…
We study the injective envelope I(X) of an operator space X, showing amongst other things that it is a self-dual C$^*-$module. We describe the diagonal corners of the injective envelope of the canonical operator system associated with X. We…
Linear spaces with an Euclidean metric are ubiquitous in mathematics, arising both from quadratic forms and inner products. Operators on such spaces also occur naturally. In recent years, the study of multivariate operator theory has made…
We study natural additional structures on real algebraic surfaces with trivial first homology mod 2 of the complexification. If the set of real points realizes the zero of the second homology mod 2 of the complexification, then the set of…
While many problems in machine learning focus on learning mappings between finite-dimensional spaces, scientific applications require approximating mappings between function spaces, i.e., operators. We study the problem of learning…
We give several applications of a recent theorem of the second author, which solved a conjecture of the first author with Hay and Neal, concerning contractive approximate identities; and another of Hay from the theory of noncommutative peak…
We consider weakly closed transitive algebras of operators containing non-zero compact operators in real Banach spaces (Lomonosov algebras). It is shown that they are naturally divided in three classes: the algebras of real, complex and…
We propose an approach to image processing related to algebraic operators acting in the space of images. In view of the interest in the applications in optics and computer science, mathematical aspects of the paper have been simplified as…
Families of operator identities appeared as a consequence of an existence of finite-dimensional representation of (super) Lie algebras of first-order differential operators and $q$-deformed (quantum) algebras of first-order…