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Dear Colleagues,

It is well known that applied functional analysis is important in most applied research fields, and its influence has grown in recent decades. Most research papers have used techniques, ideas, notions, and methods of applied functional analysis. Thus, the aim of this Special Issue is to focus on both pure mathematical tools and their applications. For this Special Issue, the submission of original research articles and reviews is welcome. Research areas may include (but are not limited to) the following: geometry of Banach spaces, functional equations, summability, statistical and ideal convergence, partial orders, lineability, and all related applications.

We look forward to receiving your contributions.

Prof. Dr. Chiming Chen
Guest Editor

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Published Papers (3 papers)

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Research

16 pages, 286 KB

Open AccessArticle

The Perturbation of the Sub-Noncommutative Pseudo-Browder Essential Spectrum of Bounded Upper Triangular Operator Matrices

by Min Su and Deyu Wu

Axioms 2026, 15(4), 299; https://doi.org/10.3390/axioms15040299 - 20 Apr 2026

Viewed by 136

Abstract

Let

ε > 0

and

TB (X \times X)

be the Banach algebra of all

2 \times 2

bounded upper triangular operator matrices on a separable Hilbert space

X \times X

. In this paper, we first establish the spectrum equalities [...] Read more.

Let

ε > 0

and

TB (X \times X)

be the Banach algebra of all

2 \times 2

bounded upper triangular operator matrices on a separable Hilbert space

X \times X

. In this paper, we first establish the spectrum equalities for special cases of upper triangular operator matrices—diagonal block operator matrix

M_{0} = (\binom{A 0}{0 B})

. We obtain that

{\hat{Σ}}_{b i, ε} (M_{0}) = Σ_{b i, ε} (A) \cup Σ_{b i, ε} (B)

i \in {1, 2, 4}

, where

Σ_{b i, ε} (\cdot)

and

{\hat{Σ}}_{b i, ε} (\cdot)

denote the noncommutative pseudo-upper (resp. lower) semi-Browder essential spectrum, noncommutative pseudo-Browder essential spectrum, sub-noncommutative pseudo-upper (resp. lower) semi-Browder essential spectrum, and sub-noncommutative pseudo-Browder essential spectrum. Secondly, based on Cao and Bai’s works, we study the perturbation of the sub-noncommutative pseudo-Browder essential spectrum

{\hat{Σ}}_{b 4, ε} (\cdot)

of a 2 × 2 bounded upper triangular operator matrix

M_{C} = (\binom{A C}{0 B})

on a separable Hilbert space. We obtain that

⋂_{C \in B (X)} {\hat{Σ}}_{b 4, ε} (M_{C}) = Σ_{b 1, ε} (A) \cup Σ_{b 2, ε} (B) \cup Δ

, where

Δ = {λ \in C :

there exist

P_{i} \in B (X)

with

∥ P_{i} ∥ < ε, i \in {1, 2},

such that

α (A + P_{1} - λ I) + α (B + P_{2} - λ I) \neq β (A + P_{1} - λ I) + β (B + P_{2} - λ I)}

. Finally, we obtain

Σ_{b i, ε} (A) \cup Σ_{b i, ε} (B) = {\hat{Σ}}_{b i, ε} (M_{C}) \cup W, i \in {1, 2, 4}

, where W is the union of certain holes in

(Σ_{b i, ε} (A) \cup Σ_{b i, ε} (B)) \ {\hat{Σ}}_{b i, ε} (M_{C})

. Full article

(This article belongs to the Special Issue Theory and Applications in Functional Analysis)

14 pages, 266 KB

Open AccessArticle

On Sawyer Duality in One and Higher Dimensions

by Alberto Fiorenza, Pankaj Jain and Saujanya Mohanty

Axioms 2026, 15(4), 266; https://doi.org/10.3390/axioms15040266 - 7 Apr 2026

Viewed by 219

Abstract

We develop the Sawyer duality principle for non-increasing functions where, in the denominator, the function g is replaced by

\int_{x}^{\infty} \frac{g (t)}{t} d t

. This result complements Stepanov’s result in which g was replaced by [...] Read more.

We develop the Sawyer duality principle for non-increasing functions where, in the denominator, the function g is replaced by

\int_{x}^{\infty} \frac{g (t)}{t} d t

. This result complements Stepanov’s result in which g was replaced by

\frac{1}{x} \int_{0}^{x} g (t) d t

. We use our result and obtain Stepanov’s result for non-decreasing functions and similarly use Stepanov’s result in proving our result for non-decreasing functions. These results have also been obtained in

R^{n}

. Full article

(This article belongs to the Special Issue Theory and Applications in Functional Analysis)

28 pages, 385 KB

Open AccessArticle

Matrix Transformations of Generalized Almost Convergent Double Sequences

by Maria Zeltser and Ekrem Savas

Axioms 2026, 15(4), 247; https://doi.org/10.3390/axioms15040247 - 25 Mar 2026

Viewed by 262

Abstract

In this paper, we study matrix transformations on spaces of generalized almost convergent double sequences with powers. Extending classical results of Lorentz, Maddox, and Nanda, we characterize several classes of infinite matrices that map between Maddox’s double sequence spaces and spaces of almost convergent (to zero) double sequences with powers. Our results generalize earlier characterizations for single sequence spaces obtained by the authors in previous work, providing a structured framework for studying summability and convergence in higher dimensions. Full article

(This article belongs to the Special Issue Theory and Applications in Functional Analysis)

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