28 research outputs found
On the Orthogonal Stability of the Pexiderized Quadratic Equation
The Hyers--Ulam stability of the conditional quadratic functional equation of
Pexider type f(x+y)+f(x-y)=2g(x)+2h(y), x\perp y is established where \perp is
a symmetric orthogonality in the sense of Ratz and f is odd.Comment: 10 pages, Latex; Changed conten
Approximately Vanishing of Topological Cohomology Groups
In this paper, we establish the Pexiderized stability of coboundaries and
cocycles and use them to investigate the Hyers--Ulam stability of some
functional equations. We prove that for each Banach algebra , Banach
-bimodule and positive integer if and only if the -th
cohomology group approximately vanishes.Comment: 18 pages, minor correction
Approximate Homomorphisms of Ternary Semigroups
A mapping between ternary semigroups will be
called a ternary homomorphism if . In this paper,
we prove the generalized Hyers--Ulam--Rassias stability of mappings of
commutative semigroups into Banach spaces. In addition, we establish the
superstability of ternary homomorphisms into Banach algebras endowed with
multiplicative norms.Comment: 10 page
Orthogonalities and functional equations
In this survey we show how various notions of orthogonality appear in the theory of functional equations. After introducing some orthogonality relations, we give examples of functional equations postulated for orthogonal vectors only. We show their solutions as well as some applications. Then we discuss the problem of stability of some of them considering various aspects of the problem. In the sequel, we mention the orthogonality equation and the problem of preserving orthogonality. Last, but not least, in addition to presenting results, we state some open problems concerning these topics. Taking into account the big amount of results concerning functional equations postulated for orthogonal vectors which have appeared in the literature during the last decades, we restrict ourselves to the most classical equations
Matrix KSGNS construction and a RadonâNikodym type theorem
In this paper, we introduce the concept of completely positive matrix of linear maps on Hilbert A-modules over locally Câ-algebras and prove an analogue of Stinespring theorem for it. We show that any two minimal Stinespring representations for such matrices are unitarily equivalent. Finally, we prove an analogue of the RadonâNikodym theorem for this type of completely positive nĂn matrices. © 2017 Royal Dutch Mathematical Society (KWG
Matrix KSGNS construction and a RadonâNikodym type theorem
In this paper, we introduce the concept of completely positive matrix of linear maps on Hilbert A-modules over locally Câ-algebras and prove an analogue of Stinespring theorem for it. We show that any two minimal Stinespring representations for such matrices are unitarily equivalent. Finally, we prove an analogue of the RadonâNikodym theorem for this type of completely positive nĂn matrices. © 2017 Royal Dutch Mathematical Society (KWG