# 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

## Latest Articles (December, 2018)

### Automorphisms generated by umbral calculus on a nuclear space of entire test functions

Ferdinand Jamil, Yuri Kondratiev, Sheila Menchavez, Ludwig Streit

Methods Funct. Anal. Topology **24** (2018), no. 4, 339-348

In this paper we show that Sheffer operators, mapping monomials to certain Sheffer polynomial sequences, such as falling and rising factorials, Charlier, and Hermite polynomials extend to continuous automorphisms on the space of entire functions of first order growth and minimal type.

### On the numerical range with respect to a family of projections

Waed Dada, Joachim Kerner, Nazife Erkurşun-Özcan

Methods Funct. Anal. Topology **24** (2018), no. 4, 297-304

In this note we introduce the concept of a numerical range of a bounded linear operator on a Hilbert space with respect to a family of projections. We give a precise definition and elaborate on its connection to the classical numerical range as well as to generalizations thereof such as the quadratic numerical range, block numerical range, and product numerical range. In general, the importance of this new notion lies within its unifying aspect.

### On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator

Methods Funct. Anal. Topology **24** (2018), no. 4, 349-369

Found are conditions on a scalar type spectral operator $A$ in a complex Banach space necessary and sufficient for all weak solutions of the evolution equation \begin{equation*} y'(t)=Ay(t),\quad t\ge 0, \end{equation*} to be strongly Gevrey ultradifferentiable of order $\beta\ge 1$, in particular analytic or entire, on $[0,\infty)$. Certain inherent smoothness improvement effects are analyzed.

### Lacunary $\mathcal{I}$-convergent and lacunary $\mathcal{I}$-bounded sequence spaces defined by a Musielak-Orlicz function over $n$-normed spaces

Methods Funct. Anal. Topology **24** (2018), no. 4, 370-380

In the present paper we defined $\mathcal{I}$-convergent and $\mathcal{I}$-bounded sequence spaces defined by a Musielak-Orlicz function $\mathcal{M} = (M_k)$ over $n$-normed spaces. We also make an effort to study some topological properties and prove some inclusion relation between these spaces.