non-Archimedean Banach Spaces Research Articles

On pencil of bounded linear operators on non-archimedean Banach spaces

In this paper, we introduce and check some properties of pseudospectrum and some approximation of a pencil of bounded linear operators on non-archimedean Banach Spaces. Our main result extends some results for a pencil of bounded linear operators on non-archimedean Banach spaces and we give some examples to support our work.

Hyperstability of the General Linear Functional Equation in Non-Archimedean Banach Spaces

Hyperstability of the General Linear Functional Equation in Non-Archimedean Banach Spaces

On the operator equations ABA = A 2 and BAB = B 2 on non-Archimedean Banach spaces

Abstract Let X X and Y Y be non-Archimedean Banach spaces over K {\mathbb{K}} , A ∈ B ( X , Y ) A\in B\left(X,Y) and B ∈ B ( Y , X ) B\in B\left(Y,X) such that A B A = A 2 ABA={A}^{2} and B A B = B 2 . BAB={B}^{2}. In this article, we investigate some properties of the operator equations A B A = A 2 ABA={A}^{2} and B A B = B 2 BAB={B}^{2} , and many common basic properties of I Y − A B {I}_{Y}-AB and I X − B A {I}_{X}-BA are given. In particular, if X X and Y Y are Banach spaces over a spherically complete field K , {\mathbb{K}}, then N ( I Y − A B ) N\left({I}_{Y}-AB) is a complemented subspace of Y Y if and only if N ( I X − B A ) N\left({I}_{X}-BA) is a complemented subspace of X . X. Finally, we give some examples to illustrate our work.

Some integrals for groups of bounded linear operators on finite-dimensional non-Archimedean Banach spaces

In this paper, we extend the Volkenborn integral and Shnirelman integral for groups of bounded linear operators on finite-dimensional non-Archimedean Banach spaces over $\mathbb{Q}_{p}$ and $\mathbb{C}_{p}$ respectively. When the ground field is a complete non-Archimedean valued field, which is also algebraically closed, we give some functional calculus for groups of infinitesimal generator $A$ such that $A$ is a nilpotent operator on finite-dimensional non-Archimedean Banach spaces.

Correction to: Some results of essential spectra of sum of two bounded linear operators in non-Archimedean Banach space

Correction to: Some results of essential spectra of sum of two bounded linear operators in non-Archimedean Banach space

Some results of essential spectra of sum of two bounded linear operators in non-Archimedean Banach space

Some results of essential spectra of sum of two bounded linear operators in non-Archimedean Banach space

Fixed Point Approach: Ulam Stability Results of Functional Equation in Non-Archimedean Fuzzy φ-2-Normed Spaces and Non-Archimedean Banach Spaces

In this work, we introduce a new type of generalized mixed-type quadratic-additive functional equation and obtain its general solution. The main goal of this work is to investigate Ulam stability of this mixed type of quadratic-additive functional equation in the setting of non-Archimedean fuzzy φ-2-normed space and non-Archimedean Banach space using the direct and fixed point approaches by taking into our account two cases: even mapping and odd mapping.

Relative boundedness in non-Archimedean Banach spaces

This paper treats general unbounded operators, closed operators, and relative boundedness in non-Archimedean Banach spaces.

Generalized Stability of the Quadratic Type λ-Functional Equation with 3k-Variables in Non-Archimedean Banach Space and Non-Archimedean Random Normed Space

Generalized Stability of the Quadratic Type λ-Functional Equation with 3k-Variables in Non-Archimedean Banach Space and Non-Archimedean Random Normed Space

Essential spectra in non-Archimedean fields

In the paper we extend some aspects of the essential spectra theory of linear operators acting in non-Archimedean (or p-adic) Banach spaces. In particular, we establish sufficient conditions for the relations between the essential spectra of the sum of two bounded linear operators and the union of their essential spectra. Moreover, we give essential prerequisites by studying the duality between p-adic upper and p-adic lower semi-Fredholm operators. We close this paper by giving some properties of the essential spectra.

Spectral analysis of special perturbations of diagonal operators on non-Archimedean Banach spaces

Spectral analysis of special perturbations of diagonal operators on non-Archimedean Banach spaces

A formula for gap between $$\mathbb {K}$$-relatively bounded operator matrices in non-Archimedean Banach spaces

A formula for gap between $$\mathbb {K}$$-relatively bounded operator matrices in non-Archimedean Banach spaces

Spectral analysis for finite rank perturbation of diagonal operator in non-archimedean Banach space of countable type

In this paper we are concerned with the spectral analysis for the classes of finte rank perturbations of diagonal operators in the form A = D+F where D is a diagonal operator and F = u’1 ⊗v’1+...+u’m ⊗vm is an operator of finite rank in the non-archimedean Banach space of countable type. We compute the spectrum of A using the theory of Fredholm operators in non archimedean setting and the concept of essential spectrum for linear operators.

Some spectral sets of linear operators pencils on non-archimedean Banach spaces

In this paper, we define the notions of trace pseudo-spectrum, ε−determinant spectrum, and ε−trace of bounded linear operator pencils on non-Archimedean Banach spaces. Many results are proved about trace pseudo-spectrum, ε−determinant spectrum, and ε−trace of bounded linear operator pencils on non-Archimedean Banach spaces. Examples are given to support our work.

$C$-groups and mixed $C$-groups of bounded linear operators on non-archimedean Banach spaces

$C$-groups and mixed $C$-groups of bounded linear operators on non-archimedean Banach spaces

Ulam-Hyers Stability Results of λ -Quadratic Functional Equation with Three Variables in Non-Archimedean Banach Space and Non-Archimedean Random Normed Space

In this paper, we introduce the λ -quadratic functional equation with three variables and obtain its general solution. The main aim of this work is to examine the Ulam-Hyers stability of this functional equation in non-Archimedean Banach space by using direct and fixed point techniques and examine the stability results in non-Archimedean random normed space.

A note on pencil of bounded linear operators on non-archimedean Banach spaces

A note on pencil of bounded linear operators on non-archimedean Banach spaces

Generalized Hyers-Ulam-Rassias type stability of the with 2k-variable quadratic functional inequalities in non-Archimedean Banach spaces and Banach spaces

Generalized Hyers-Ulam-Rassias type stability of the with 2k-variable quadratic functional inequalities in non-Archimedean Banach spaces and Banach spaces

P-adic discrete semigroup of contractions

Let A ∈ B(X) be a spectral operator on a non-archimedean Banach space over Cp. In this paper, we give a necessary and sufficient condition on the resolvent of A so that the discrete semigroup consisting of powers of A is contractions.

Hyers-Ulam Stability of Quadratic Functional Equation Based on Fixed Point Technique in Banach Spaces and Non-Archimedean Banach Spaces

In this paper, the authors investigate the Hyers–Ulam stability results of the quadratic functional equation in Banach spaces and non-Archimedean Banach spaces by utilizing two different techniques in terms of direct and fixed point techniques.