Results 41 to 50 of about 1,201 (92)
Spectral integration and spectral theory for non‐Archimedean Banach spaces
International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 7, Page 421-442, 2002., 2002 Banach algebras over arbitrary complete non‐Archimedean fields are considered such that operators may be nonanalytic. There are different types of Banach spaces over non‐Archimedean fields. We have determined the spectrum of some closed commutative subalgebras of the Banach algebra ℒ(E) of the continuous linear operators on a free Banach space E ...
S. Ludkovsky, B. Diarra
wiley +1 more source
On unbounded commuting Jacobi operators and some related issues
Concrete Operators, 2019 We consider the situations, when two unbounded operators generated by infinite Jacobi matrices, are self-adjoint and commute. It is found that if two Jacobi matrices formally commute, then two corresponding operators are either self-adjoint and commute ...
Osipov Andrey
doaj +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.For the Weinstein Laplacian considered on the Hilbert space which makes it a self‐adjoint operator, the Von Neumann spectral decomposition is given. As applications, a new integral representation for the Weinstein heat kernel is given. Also, it is proved that the spectrum of the semigroup associated with the Weinstein Laplacian is reduced to its ...
Abdelilah El Mourni +3 more
wiley +1 more source
Continuity and general perturbation of the Drazin inverse for closed linear operators
Abstract and Applied Analysis, Volume 7, Issue 6, Page 335-347, 2002., 2002 We study perturbations and continuity of the Drazin inverse of a closed linear operator A and obtain explicit error estimates in terms of the gap between closed operators and the gap between ranges and nullspaces of operators. The results are used to derive a theorem on the continuity of the Drazin inverse for closed operators and to describe the ...
N. Castro González +2 more
wiley +1 more source
Nonlocal heat equations with generalized fractional Laplacian
Advances in Nonlinear AnalysisWe study heat equations with generalized fractional Laplacian, which is defined by the spectral theory. Here we develop the existence theory for those equations. Also, we present some numerical simulations for our problems.
Kossowski Igor, Przeradzki Bogdan
doaj +1 more source
Negative Powers of Contractions Having a Strong AA+ Spectrum
Moroccan Journal of Pure and Applied Analysis, 2023 Zarrabi proved in 1993 that if the spectrum of a contraction T on a Banach space is a countable subset of the unit circle 𝕋, and if limn→+∞log(‖T−n‖)n=0{\lim _{n \to + \infty }}{{\log \left( {\left\| {{T^{ - n}}} \right\|} \right)} \over {\sqrt n ...
Esterle Jean
doaj +1 more source
Journal of Mathematics, Volume 2025, Issue 1, 2025.This paper investigates an abstract nonhomogeneous backward Cauchy problem governed by an unbounded linear operator in a Hilbert space H. The coefficient operator in the equation is assumed to be unbounded, self‐adjoint, positive, and to possess a discrete spectrum, with data prescribed at the final time t = T.
Nihed Teniou, Xian-Ming Gu
wiley +1 more source
On some properties of Banach operators
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 3, Page 149-153, 2001., 2001 A mapping α from a normed space X into itself is called a Banach operator if there is a constant k such that 0 ≤ k < 1 and ‖α2(x) − α(x)‖ ≤ k‖α(x) − x‖ for all x ∈ X. In this note we study some properties of Banach operators. Among other results we show that if α is a linear Banach operator on a normed space X, then N(α − 1) = N((α−1)2), N(α − 1)∩R(α −
A. B. Thaheem, AbdulRahim Khan
wiley +1 more source
On the generalized Kato spectrum [PDF]
, 2011 2010 Mathematics Subject Classification: 47A10.We show that the symmetric difference between the generalized Kato spectrum and the essential spectrum defined in [7] by sec(T) = {l О C ; R(lI-T) is not closed } is at most countable and we also give some
Benharrat, Mohammed, Messirdi, Bekkai
core
On the spectrum of ψ‐contracting operators
International Journal of Stochastic Analysis, Volume 14, Issue 3, Page 303-308, 2001., 2001 The spectrum σ(A) of a continuous linear operator A : E → E defined on a Banach space E, which is contracting with respect to the Hausdorff measure of noncompactness, is investigated.
Anwar A. Al-Nayef
wiley +1 more source