Results 1 to 10 of about 24 (24)

Global Perturbation of Nonlinear Eigenvalues

Advanced Nonlinear Studies, 2021
This paper generalizes the classical theory of perturbation of eigenvalues up to cover the most general setting where the operator surface 𝔏:[a,b]×[c,d]→Φ0⁢(U,V){\mathfrak{L}:[a,b]\times[c,d]\to\Phi_{0}(U,V)}, (λ,μ)↦𝔏⁢(λ,μ){(\lambda,\mu)\mapsto\mathfrak ...
López-Gómez Julián, Sampedro Juan Carlos   +1 more
doaj   +1 more source

Generalized lower characteristic involving measures of non-strict singularity

Topological Algebra and its Applications, 2023
This work establishes a connection between the class of generalized lower characteristic operators and [⋅]a{\left[\cdot ]}_{a} acting on a Banach space involving measures of non-strict singularity.
Baraket Sami, Ghorbal Anis Ben, Jeribi Aref   +2 more
doaj   +1 more source

On (m, P)-expansive operators: products, perturbation by nilpotents, Drazin invertibility

Concrete Operators, 2021
A generalisation of m-expansive Hilbert space operators T ∈ B(ℋ) [18, 20] to Banach space operators T ∈ B(𝒳) is obtained by defining that a pair of operators A, B ∈ B(𝒳) is (m, P)-expansive for some operator P ∈ B(𝒳) if Δ A,Bm(P)= (I-LARB)m(P)=∑j=0m(-1)j(
Duggal B.P.
doaj   +1 more source

Structure of n-quasi left m-invertible and related classes of operators

Demonstratio Mathematica, 2020
Given Hilbert space operators T,S∈B(ℋ)T,S\in B( {\mathcal H} ), let Δ\text{Δ} and δ∈B(B(ℋ))\delta \in B(B( {\mathcal H} )) denote the elementary operators ΔT,S(X)=(LTRS−I)(X)=TXS−X{\text{Δ}}_{T,S}(X)=({L}_{T}{R}_{S}-I)(X)=TXS-X and δT,S(X)=(
Duggal Bhagwati Prashad, Kim In Hyun
doaj   +1 more source

On the spectra of non‐selfadjoint differential operators and their adjoints in direct sum spaces

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 9, Page 557-574, 2003., 2003
The general ordinary quasidifferential expression Mp of nth order, with complex coefficients and its formal adjoint Mp+ on any finite number of intervals Ip = (ap, bp), p = 1, …, N, are considered in the setting of the direct sums of Lwp2(ap,bp)‐spaces of functions defined on each of the separate intervals.
Sobhy El-Sayed Ibrahim
wiley   +1 more source

Spectrum perturbations of compact operators in a Banach space

Open Mathematics, 2019
For an integer p ≥ 1, let Γp be an approximative quasi-normed ideal of compact operators in a Banach space with a quasi-norm NΓp(.) and the ...
Gil’ Michael
doaj   +1 more source

On the domain of selfadjoint extension of the product of Sturm‐Liouville differential operators

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 11, Page 695-709, 2003., 2003
The second‐order symmetric Sturm‐Liouville differential expressions τ1, τ2, …, τn with real coefficients are considered on the interval I = (a, b), −∞ ≤ a < b ≤ ∞. It is shown that the characterization of singular selfadjoint boundary conditions involves the sesquilinear form associated with the product of Sturm‐Liouville differential expressions and ...
Sobhy El-Sayed Ibrahim
wiley   +1 more source

Remarks on embeddable semigroups in groups and a generalization of some Cuthbert′s results

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 22, Page 1421-1431, 2003., 2003
Let (U(t)) t≥0 be a C0‐semigroup of bounded linear operators on a Banach space X. In this paper, we establish that if, for some t0 > 0, U(t0) is a Fredholm (resp., semi‐Fredholm) operator, then (U(t)) t≥0 is a Fredholm (resp., semi‐Fredholm) semigroup.
Khalid Latrach, Abdelkader Dehici
wiley   +1 more source

A spectral mapping theorem for semigroups solving PDEs with nonautonomous past

Abstract and Applied Analysis, Volume 2003, Issue 16, Page 933-951, 2003., 2003
We prove a spectral mapping theorem for semigroups solving partial differential equations with nonautonomous past. This theorem is then used to give spectral conditions for the stability of the solutions of the equations.
Genni Fragnelli
wiley   +1 more source

Kreĭn′s trace formula and the spectral shift function

International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 4, Page 239-252, 2001., 2001
Let A, B be two selfadjoint operators whose difference B − A is trace class. Kreĭn proved the existence of a certain function ξ ∈ L1(ℝ) such that tr[f(B) − f(A)] = ∫ℝf′(x)ξ(x)dx for a large set of functions f. We give here a new proof of this result and discuss the class of admissible functions.
Khristo N. Boyadzhiev
wiley   +1 more source