Research Paper Functional analysis
On the h-Jensen's operator inequality

S. S. Hashemi Karouei; M. S. Asgari; M. Shah Hosseini; N. Ghafoori Adl

Volume 11, Issue 02 , June 2022, Pages 77-83

http://dx.doi.org/10.30495/jlta.2022.1952840.1471

Abstract
  ‎In this paper‎, ‎we prove Jensen's operator inequality for an h-convex function and we point out the results for classes of continuous‎ ‎fields of operators‎. ‎Also‎, ‎some generalizations of Jensen's operator inequality and some properties of the h-convex function ...  Read More

Research Paper Algebraic topology
Topological spaces induced by homotopic distance

T. Vergili; A. Borat

Volume 11, Issue 02 , June 2022, Pages 85-91

http://dx.doi.org/10.30495/jlta.2022.1955292.1482

Abstract
  ‎Topological complexity which plays an important role in motion planning problem can be generalized to homotopic distance $\mathrm{D}$ as introduced in \cite{MVML}‎. ‎In this paper‎, ‎we study the homotopic distance and mention that it can be realized as a pseudometric on $\mathrm{Map}(X,Y)$‎. ...  Read More

Research Paper Operator theory
On equality of complete positivity and complete copositivity of positive map

C. A. Winda; N. B. Okelo; O. Ongati

Volume 11, Issue 02 , June 2022, Pages 93-108

http://dx.doi.org/10.30495/jlta.2022.1949354.1458

Abstract
  ‎In this paper we construct a $2$-positive map from $\ma_4(\Complex)$ to $\ma_5(\Complex)$ and state the conditions under which the map is positive and completely positive (copositivity of positive)‎. ‎The construction allows us to create a decomposable map, where the Choi matrix of complete ...  Read More

Research Paper Functional analysis
On the continuity of some linear maps on certain Banach algebras

H. Farhadi; E. Ghaderi

Volume 11, Issue 02 , June 2022, Pages 109-122

http://dx.doi.org/10.30495/jlta.2022.1952747.1470

Abstract
  ‎Let $\mathcal{A}$ and $\mathcal{U}$ be Banach algebras‎, ‎$\theta$ be a nonzero character on $\mathcal{A}$ and let ${\mathcal{A}}\times_{\theta}{\mathcal{U}}$ be the corresponding Lau product Banach algebra‎. ‎In this paper we investigate derivations and multipliers of ${\mathcal{A}}\times_{\theta}{\mathcal{U}}$ ...  Read More

Research Paper General topology
Bornological linearly topologized modules over a discrete valuation ring

D. P. Pombo Jr.

Volume 11, Issue 02 , June 2022, Pages 123-128

http://dx.doi.org/10.30495/jlta.2022.1953833.1477

Abstract
  ‎In this work the notion of a bornological linearly topologized mo\-dule over a discrete valuation ring is introduced and it is shown that certain semimetrizable linearly topologized modules are bornological‎. ‎The main result is a characterization of bornological linearly topologized modules‎, ...  Read More

Research Paper Operator theory
Equivariant homologies for operator algebras; a survey

A. Shirinkalam

Volume 11, Issue 02 , June 2022, Pages 129-142

http://dx.doi.org/10.30495/jlta.2022.1957929.1493

Abstract
  ‎This is a survey of a variety of equivariant (co)homology theories for operator algebras‎. ‎We briefly discuss a background on equivariant Hochschild cohomology‎. ‎We discuss a notion of equivariant $ L^2 $-cohomology and equivariant $ L^2 $-Betti numbers for subalgebras of a von ...  Read More