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1
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Perturbation of the spectrum οf an essentially selfadjoint operator

100%
Pokrzywa A.
Applicationes Mathematicae
|
1993-1995
|
tom 22
|
nr 1
75-89
EN
The aim of this paper is to find estimates of the Hausdorff distance between the spectra of two nonselfadjoint operators. The operators considered are assumed to have their imaginary parts in some normed ideal of compact operators. In the case of the classical Schatten ideals the estimates are given explicitly.
2
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Some problems concerning different types of vector valued almost periodic functions

82%
Basit B.
Instytut Matematyczny Polskiej Akademii Nauk
EN
Abstract We study some problems concerning derivatives and indefinite integrals of elements of wide classes of functions (including almost periodic, recurrent, almost automorphic and Eberlein almost periodic functions). We introduce a notion of a spectrum of a function with respect to a class of functions. This notion enables us to investigate almost periodicity of the bounded solutions of certain functional equations.
3
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On the joint spectral radius

80%
Müller V.
Annales Polonici Mathematici
|
1997
|
tom 66
|
nr 1
173-182
EN
We prove the $𝓁_p$-spectral radius formula for n-tuples of commuting Banach algebra elements
4
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Weak invertibility and strong spectrum

80%
Meyer M. J.
Studia Mathematica
|
1993
|
tom 105
|
nr 3
255-269
EN
A notion of weak invertibility in a unital associative algebra A and a corresponding notion of strong spectrum of an element of A is defined. It is shown that many relationships between the Jacobson radical, the group of invertibles and the spectrum have analogues relating the strong radical, the set of weakly invertible elements and the strong spectrum. The nonunital case is also discussed. A characterization is given of all (submultiplicative) norms on A in which every modular maximal ideal M ⊆ A is closed.
5
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On the invertibility of isometric semigroup representations

80%
Batty C. J. K., Greenfield D. A.
Studia Mathematica
|
1994
|
tom 110
|
nr 3
235-250
EN
Let T be a representation of a suitable abelian semigroup S by isometries on a Banach space. We study the spectral conditions which will imply that T(s) is invertible for each s in S. On the way we analyse the relationship between the spectrum of T, Sp(T,S), and its unitary spectrum $Sp_{u}(T,S)$. For $S = ℤ^{n}_{+}$ or $ℝ^{n}_{+}$, we establish connections with polynomial convexity.
6
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Product $ℤ^d$-actions on a Lebesgue space and their applications

80%
Filipowicz I.
Studia Mathematica
|
1997
|
tom 122
|
nr 3
289-298
EN
We define a class of $ℤ^d$-actions, d ≥ 2, called product $ℤ^d$-actions. For every such action we find a connection between its spectrum and the spectra of automorphisms generating this action. We prove that for any subset A of the positive integers such that 1 ∈ A there exists a weakly mixing $ℤ^d$-action, d≥2, having A as the set of essential values of its multiplicity function. We also apply this class to construct an ergodic $ℤ^d$-action with Lebesgue component of multiplicity $2^d k$, where k is an arbitrary positive integer.
7
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Subnormal operators of Hardy type

80%
Rudol K.
Banach Center Publications
|
1997
|
tom 38
|
nr 1
315-324
8
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On the spectrum of A(Ω) and $H^∞(Ω)$

80%
Cegrell U.
Annales Polonici Mathematici
|
1993
|
tom 58
|
nr 2
193-199
EN
We study some properties of the maximal ideal space of the bounded holomorphic functions in several variables. Two examples of bounded balanced domains are introduced, both having non-trivial maximal ideals.
9
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Characterizing spectra of closed operators through existence of slowly growing solutions of their Cauchy problems

80%
Zhong Huang S.
Studia Mathematica
|
1995
|
tom 116
|
nr 1
23-41
EN
Let A be a closed linear operator in a Banach space E. In the study of the nth-order abstract Cauchy problem $u^{(n)}(t) = Au(t)$, t ∈ ℝ, one is led to considering the linear Volterra equation (AVE) $u(t) = p(t) + A ʃ_{0}^{t} a(t-s)u(s)ds$, t ∈ ℝ, where $a(·) ∈ L_{loc}^{1}(ℝ)$ and p(·) is a vector-valued polynomial of the form $p(t) = ∑_{j=0}^n 1/(j!) x_j t^j$ for some elements $x_j ∈ E$. We describe the spectral properties of the operator A through the existence of slowly growing solutions of the (AVE). The main tool is the notion of Carleman spectrum of a vector-valued function. Moreover, an extension of a theorem of Pólya in complex analysis is obtained and applied to the individual "Ax = 0" and "Tx = x" problem.
10
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Resolvent and spectrum of a nonselfadjoint differential operator in a Hilbert space

80%
Gil’ M.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
|
2012
|
tom 66
|
nr 1
EN
We consider a second order regular differential operator whose coefficients are nonselfadjoint bounded operators acting in a Hilbert space. An estimate for the resolvent and a bound for the spectrum are established. An operator is said to be stable if its spectrum lies in the right half-plane. By the obtained bounds, stability and instability conditions are established.
11
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Spectra of abelian wekly associative lattice groups

71%
Rachůnek J.
Discussiones Mathematicae - General Algebra and Applications
|
2000
|
tom 20
|
nr 1
51-61
EN
The notion of a weakly associative lattice group is a generalization of that of a lattice ordered group in which the identities of associativity of the lattice operations join and meet are replaced by the identities of weak associativity. In the paper, the spectral topologies on the sets of straightening ideals (and on some of their subsets) of abelian weakly associative lattice groups are introduced and studied.
12
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Limit points of eigenvalues of truncated unbounded tridiagonal operators

71%
Ifantis E. K., Kokologiannaki C. G., Petropoulou E.
Open Mathematics
|
2007
|
tom 5
|
nr 2
335-344
EN
Let T be a self-adjoint tridiagonal operator in a Hilbert space H with the orthonormal basis {e n}n=1∞, σ(T) be the spectrum of T and Λ(T) be the set of all the limit points of eigenvalues of the truncated operator T N. We give sufficient conditions such that the spectrum of T is discrete and σ(T) = Λ(T) and we connect this problem with an old problem in analysis.
13
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Closed operators affiliated with a Banach algebra of operators

71%
Barnes B. A.
Studia Mathematica
|
1991-1992
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tom 101
|
nr 3
215-240
EN
Let ℬ be a Banach algebra of bounded linear operators on a Banach space X. If S is a closed operator in X such that (λ - S)^{-1} ∈ ℬ for some number λ, then S is affiliated with ℬ. The object of this paper is to study the spectral theory and Fredholm theory relative to ℬ of an operator which is affiliated with ℬ. Also, applications are given to semigroups of operators which are contained in ℬ.
14
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Essential spectra of weighted composition operators with hyperbolic symbols

71%
Hyvärinen O., Nieminen I.
Concrete Operators
|
2015
|
tom 2
|
nr 1
EN
In this paperwe study both the spectra and the essential spectra ofweighted composition operators on Hardy spaces Hp(ⅅ), standard weighted Bergman spaces Apα(ⅅ) and weighted H∞1-type spaces when the symbols are of hyperbolic type
15
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Nonsingular unicyclic mixed graphs with at most three eigenvalues greater than two

71%
Gong S.-C., Fan Y.-Z.
Discussiones Mathematicae Graph Theory
|
2007
|
tom 27
|
nr 1
69-82
EN
This paper determines all nonsingular unicyclic mixed graphs on at least nine vertices with at most three Laplacian eigenvalues greater than two.
16
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A geometric estimate for a periodic Schrödinger operator

71%
Friedrich T.
Colloquium Mathematicum
|
2000
|
tom 83
|
nr 2
209-216
EN
We estimate from below by geometric data the eigenvalues of the periodic Sturm-Liouville operator $-4{d^2}/{ds^2} + κ^2(s)$ with potential given by the curvature of a closed curve.
17
Content available remote

Spectrum of commutative Banach algebras and isomorphism of C*-algebras related to locally compact groups

61%
Hu Z.
Studia Mathematica
|
1998
|
tom 129
|
nr 3
207-223
EN
Let A be a semisimple commutative regular tauberian Banach algebra with spectrum $Σ_A$. In this paper, we study the norm spectra of elements of $\overline{span} Σ_A$ and present some applications. In particular, we characterize the discreteness of $Σ_A$ in terms of norm spectra. The algebra A is said to have property (S) if, for all $φ ∈ \overline{\span} Σ_A \ {0}$, φ has a nonempty norm spectrum. For a locally compact group G, let $ℳ_2^{d}(Ĝ)$ denote the C*-algebra generated by left translation operators on $L^2(G)$ and $G_{d}$ denote the discrete group G. We prove that the Fourier algebra $A(G)$ has property (S) iff the canonical trace on $ℳ_2^{d}(Ĝ)$ is faithful iff $ℳ_2^{d} (Ĝ)≅ ℳ_2^{d} (Ĝ_{d})$. This provides an answer to the isomorphism problem of the two C*-algebras and generalizes the so-called "uniqueness theorem" on the group algebra $L^1(G)$ of a locally compact abelian group G. We also prove that $G_{d}$ is amenable iff G is amenable and the Figà-Talamanca-Herz algebra $A_p(G)$ has property (S) for all p.
18
Content available remote

Quantum graph spectra of a graphyne structure

61%
Do N. T., Kuchment P.
Nanoscale Systems: Mathematical Modeling, Theory and Applications
|
2013
|
tom 2
107-123
EN
We study the dispersion relations and spectra of invariant Schrödinger operators on a graphyne structure (lithographite). In particular, description of different parts of the spectrum, band-gap structure, and Dirac points are provided.
19
Content available remote

On Spectra Of Variants Of The Corona Of Two Graphs And Some New Equienergetic Graphs

61%
Adiga C., Rakshith B. R.
Discussiones Mathematicae Graph Theory
|
2016
|
tom 36
|
nr 1
127-140
EN
Let G and H be two graphs. The join G ∨ H is the graph obtained by joining every vertex of G with every vertex of H. The corona G ○ H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining the i-th vertex of G to every vertex in the i-th copy of H. The neighborhood corona G★H is the graph obtained by taking one copy of G and |V (G)| copies of H and joining the neighbors of the i-th vertex of G to every vertex in the i-th copy of H. The edge corona G ◇ H is the graph obtained by taking one copy of G and |E(G)| copies of H and joining each terminal vertex of i-th edge of G to every vertex in the i-th copy of H. Let G1, G2, G3 and G4 be regular graphs with disjoint vertex sets. In this paper we compute the spectrum of (G1 ∨ G2) ∪ (G1 ★ G3), (G1 ∨ G2) ∪ (G2 ★ G3) ∪ (G1 ★ G4), (G1 ∨G2)∪(G1 ○G3), (G1 ∨G2)∪(G2 ○G3)∪(G1 ○G4), (G1 ∨G2)∪(G1 ◇G3), (G1 ∨ G2) ∪ (G2 ◇ G3) ∪ (G1 ◇ G4), (G1 ∨ G2) ∪ (G2 ○ G3) ∪ (G1 ★ G3), (G1 ∨ G2) ∪ (G2 ○ G3) ∪ (G1 ◇ G4) and (G1 ∨ G2) ∪ (G2 ★ G3) ∪ (G1 ◇ G4). As an application, we show that there exist some new pairs of equienergetic graphs on n vertices for all n ≥ 11.
20
Content available remote

Spectra of partial integral operators with a kernel of three variables

51%
Eshkabilov Y.
Open Mathematics
|
2008
|
tom 6
|
nr 1
149-157
EN
Let Ω= [a, b] × [c, d] and T 1, T 2 be partial integral operators in $$ C $$(Ω): (T 1 f)(x, y) = $$ \mathop \smallint \limits_a^b $$ k 1(x, s, y)f(s, y)ds, (T 2 f)(x, y) = $$ \mathop \smallint \limits_c^d $$ k 2(x, ts, y)f(t, y)dt where k 1 and k 2 are continuous functions on [a, b] × Ω and Ω × [c, d], respectively. In this paper, concepts of determinants and minors of operators E−τT 1, τ ∈ ℂ and E−τT 2, τ ∈ ℂ are introduced as continuous functions on [a, b] and [c, d], respectively. Here E is the identical operator in C(Ω). In addition, Theorems on the spectra of bounded operators T 1, T 2, and T = T 1 + T 2 are proved.
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