scholarly journals On mixed C-semigroups of operators on Banach spaces

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2673-2682
Author(s):  
Masoud Mosallanezhad ◽  
Mohammad Janfada
Keyword(s):  
Banach Spaces ◽  
Parameter Family ◽  
Linear Operators ◽  
Semigroups Of Operators ◽  
Semigroup Of Operators ◽  
Cauchy Equation ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cosine Families ◽  
Special Case

In this paper an H-generalized Cauchy equation S(t+s)C = H(S(s),S(t)) is considered, where {S(t)}t?0 is a one parameter family of bounded linear operators and H : B(X) x B(X) ? B(X) is a function. In the special case, when H(S(s), S(t))=S(s)S(t)+D(S(s)-T(s))(S(t)-T(t)) with D ? B(X), solutions of H-generalized Cauchy equation are studied, where {T(t)}t?0 is a C-semigroup of operators. Also a similar equations are studied on C-cosine families and integrated C-semigroups.

On the null spaces of linear Fredholm operators depending on several parameters

1978 ◽  
Vol 84 (1) ◽  
pp. 131-142 ◽  
Author(s):  
M. Shearer
Keyword(s):  
Banach Spaces ◽  
Fredholm Operator ◽  
Bifurcation Theory ◽  
Null Space ◽  
Parameter Family ◽  
Linear Operators ◽  
Fredholm Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear

AbstractLet X, Y be real Banach spaces, and let = {f(λ):λ ∈ m} be an m-parameter family of bounded linear operators from X to Y, with f(λ) depending continuously on λ. The cases m = 1 and m = 2 are considered, and conditions on are found which determine the null space of f(λ) for all λ near a given λ0 such that f(λ0): X → Y is a Fredholm operator. The results obtained are shown to be of particular interest in perturbed bifurcation theory.

A note on C0-groups and C-groups on non-archimedean Banach spaces

2020 ◽  
pp. 2150104 ◽  
Author(s):  
A. El Amrani ◽  
A. Blali ◽  
J. Ettayb ◽  
M. Babahmed
Keyword(s):  
Banach Spaces ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cosine Families ◽  
Valued Field

In this paper, we introduce new classes of linear operators so called [Formula: see text]-groups, [Formula: see text]-groups and cosine families of bounded linear operators on non-archimedean Banach spaces over non-archimedean complete valued field [Formula: see text]. We show some results about it.

scholarly journals On Regularized Quasi-Semigroups and Evolution Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-13
Author(s):  
M. Janfada
Keyword(s):  
Banach Spaces ◽  
Infinitesimal Generator ◽  
Evolution Equations ◽  
Linear Operators ◽  
Semigroups Of Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Abstract Evolution Equations ◽  
Regularized Semigroups

We introduce the notion of regularized quasi-semigroup of bounded linear operators on Banach spaces and its infinitesimal generator, as a generalization of regularized semigroups of operators. After some examples of such quasi-semigroups, the properties of this family of operators will be studied. Also some applications of regularized quasi-semigroups in the abstract evolution equations will be considered. Next some elementary perturbation results on regularized quasi-semigroups will be discussed.

Cosine families of bounded linear operators on non-archimedean Banach spaces

2021 ◽  
Vol Accepted ◽  
Author(s):  
J. Ettayb ◽  
A. Blali ◽  
A. El amrani ◽  
R. A. Hassani
Keyword(s):  
Banach Spaces ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Cosine Families

Duality of the distance to closed operator ideals

2003 ◽  
Vol 133 (1) ◽  
pp. 197-212 ◽  
Author(s):  
Hans-Olav Tylli
Keyword(s):  
Banach Spaces ◽  
Closed Operator ◽  
Operator Ideal ◽  
Linear Operators ◽  
Distance Functions ◽  
Approximation Properties ◽  
Operator Ideals ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Special Operator

Special operator-ideal approximation properties (APs) of Banach spaces are employed to solve the problem of whether the distance functions S ↦ dist(S*, I(F*, E*)) and S ↦ dist(S, I*(E, F)) are uniformly comparable in each space L(E, F) of bounded linear operators. Here, I*(E, F) = {S ∈ L(E, F) : S* ∈ I(F*, E*)} stands for the adjoint ideal of the closed operator ideal I for Banach spaces E and F. Counterexamples are obtained for many classical surjective or injective Banach operator ideals I by solving two resulting ‘asymmetry’ problems for these operator-ideal APs.

scholarly journals Uniqueness of the maximal ideal of operators on the ℓp-sum of ℓ∞n (n ∈ ) for 1 < p < ∞

2016 ◽  
Vol 160 (3) ◽  
pp. 413-421 ◽  
Author(s):  
TOMASZ KANIA ◽  
NIELS JAKOB LAUSTSEN
Keyword(s):  
Banach Space ◽  
Recent Result ◽  
Banach Algebra ◽  
Banach Spaces ◽  
Maximal Ideal ◽  
American Mathematical Society ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Unique Maximal Ideal

AbstractA recent result of Leung (Proceedings of the American Mathematical Society, 2015) states that the Banach algebra ℬ(X) of bounded, linear operators on the Banach space X = (⊕n∈$\mathbb{N}$ ℓ∞n)ℓ1 contains a unique maximal ideal. We show that the same conclusion holds true for the Banach spaces X = (⊕n∈$\mathbb{N}$ ℓ∞n)ℓp and X = (⊕n∈$\mathbb{N}$ ℓ1n)ℓp whenever p ∈ (1, ∞).

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