Related papers: Fra\"{i}ss\'e theory in operator algebras
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…
The general Galois theory for functions and relational constraints over arbitrary sets described in the authors' previous paper is refined by imposing algebraic conditions on relations.
By appropriate choices of elements in the underlying iterated function system, methodology of fractal interpolation entitles one to associate a family of continuous self-referential functions with a prescribed real-valued continuous…
The notion of extension of a given $C^*$-category $C$ by a $C^*$-algebra $A$ is introduced. In the commutative case $A = C(\Omega)$, the objects of the extension category are interpreted as fiber bundles over $\Omega$ of objects belonging…
We extend the usual theory of universal C*-algebras from generators and relations in order to allow some relations to be described using the strong operator topology. In particular, we can allow some infinite sum relations. We prove a…
In this paper, we show how a class of operators used in the analysis of measures from wavelets and iterated function systems may be understood from a special family of representations of Cuntz algebras.
The mirror extensions for vertex operator algebras are studied. Two explicit examples which are not simple current extensions of some affine vertex operator algebras of type $A$ are given.
We prove a continuous-parameter version of the recent theorem of Katznelson-Tzafiri type for power-bounded operators which have a bounded calculus for analytic Besov functions. We also show that the result can be extended to some operators…
We provide a general theoretical framework allowing us to extend the classical Lie theory for partial differential equations to the case of equations of fractional order. We propose a general prolongation formula for the study of Lie…
Fix a unital $C^*$-algebra $\mathscr{A}$, and write $\mathscr{A}_{sa}$ for the set of self-adjoint elements of $\mathscr{A}$. Also, if $f:\mathbb{R}\to\mathbb{C}$ is a continuous function, then write…
Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this…
We develop the fine structure theory of operator-premice. These are a generalization of standard premice, in which an abstract operator $F$ is used to form the successor steps in the internal hierarchy of the premouse, instead of Jensen's…
The theory of abstract Friedrichs operators, introduced by Ern, Guermond and Caplain (2007), proved to be a successful setting for studying positive symmetric systems of first order partial differential equations (Friedrichs, 1958),…
This article is devoted to the investigation of $B^*$-algebras, dual and annihilator ultranormed algebras. Their structure is studied in the paper. Extensions of algebras and fields are considered and using them core radicals and radicals…
We extend and deepen the theory of functional calculus for semigroup generators, based on the algebra $\mathcal B$ of analytic Besov functions, which we initiated in a previous paper. In particular, we show that our construction of the…
It is shown that the *-algebra of all (closed densely defined linear) operators affiliated with a finite type I von Neumann algebra admits a unique center-valued trace, which turns out to be, in a sense, normal. It is also demonstrated that…
We develop a systematic study of the schur tensor product both in the category of operator spaces and in that of $C^*$-algebras.
This paper shows how the use of Structural Operational Semantics (SOS) in the style popularized by the process-algebra community can lead to a more succinct and useful construction for building finite automata from regular expressions. Such…
There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field…
In this paper we show that the Rees algebra can be made into a functor on modules over a ring in a way that extends its classical definition for ideals. The Rees algebra of a module M may be computed in terms of a "maximal" map f from M to…