# Methods of Functional Analysis and Topology

Editors-in-Chief: Yu. M. Berezansky, Yu. G. Kondratiev
ISSN: 1029-3531 (Print) 2415-7503 (Online)

Methods of Functional Analysis and Topology (MFAT), founded in 1995, is a peer-reviewed arXiv overlay journal publishing original articles and surveys on general methods and techniques of functional analysis and topology with a special emphasis on applications to modern mathematical physics.

MFAT is an open access journal, free for authors and free for readers.

MFAT is indexed in: MathSciNet, zbMATH, Scopus, Web of Science, DOAJ, Google Scholar

Volumes: 25 | Issues: 94 | Articles: 724 | Authors: 526

## Latest Articles (June, 2019)

### Subscalarity of $k$-quasi-class $A$ operators

M. H. M. Rashid

Methods Funct. Anal. Topology 25 (2019), no. 2, 177-188

In this paper, we show that every $k$-quasi-class $A$ operator has a scalar extension and give some spectral properties of the scalar extensions of $k$-quasi-class $A$ operators. As a corollary, we get that such an operator with rich spectrum has a nontrivial invariant subspace.

### Abstract formulation of the Cole-Hopf transform

Yoritaka Iwata

Methods Funct. Anal. Topology 25 (2019), no. 2, 142-151

Operator representation of Cole-Hopf transform is obtained based on the logarithmic representation of infinitesimal generators. For this purpose the relativistic formulation of abstract evolution equation is introduced. Even independent of the spatial dimension, the Cole-Hopf transform is generalized to a transform between linear and nonlinear equations defined in Banach spaces. In conclusion a role of transform between the evolution operator and its infinitesimal generator is understood in the context of generating nonlinear semigroup.

### On eigenvalues of banded matrices

Methods Funct. Anal. Topology 25 (2019), no. 2, 98-103

In the paper, asymptotics for eigenvalues of Hermitian, compact operators, generated by infinite, banded matrices is obtained in terms of the asymptotics of their matrix entries. Analogues for banded matrices of Gershgorin's disks theory are discussed.

### Operators preserving orthogonality on Hilbert $\it{K}(H)$-modules

Methods Funct. Anal. Topology 25 (2019), no. 2, 189-194

In this paper, we study the class of orthogonality preserving operators on a Hilbert $\it{K(H)}$-module $W$ and show that an operator $T$ on $W$ is orthogonality preserving if and only if it is orthogonality preserving on a special dense submodule of $W$. Then we apply this fact to show that an orthogonality preserving operator $T$ is normal if and only if $T^*$ is orthogonality preserving.