Spectral properties of compact multiparameter operators

1984 ◽  
Vol 98 (3-4) ◽  
pp. 291-303 ◽  
Author(s):  
Paul Binding ◽  
Patrick J. Browne ◽  
Lawrence Turyn
Keyword(s):  
Hilbert Space ◽  
Spectral Properties ◽  
Symmetric Operator ◽  
Convex Set ◽  
Complex Hilbert Space ◽  
Recession Cone ◽  
Maximal Eigenvalue ◽  
Open Convex

SynopsisLetbe, for each λ∈ℝk, a compact symmetric operator on a complex Hilbert space. Let the“fundamental” eigenset Z be denned by the relation λ∈Z if and only if W(λ) has maximal eigenvalue one. Conditions are given for Z to be the boundary of an open convex set P. A detailed investigation is given of the structure of P, including its recession cone and its representations as intersections of half-spaces.

scholarly journals A Certain Subclass of Multivalent Analytic Functions with Negative Coefficients for Operator on Hilbert Space

2019 ◽  
pp. 355-364
Author(s):  
Asraa Abdul Jaleel Husien
Keyword(s):  
Hilbert Space ◽  
Analytic Functions ◽  
Convex Set ◽  
Extreme Points ◽  
Complex Hilbert Space ◽  
Coefficient Estimates ◽  
Geometric Properties

In the present work, we introduce and study a certain subclass for multivalent analytic functions with negative coefficients defined on complex Hilbert space. We establish a number of geometric properties, like, coefficient estimates, convex set, extreme points and radii of starlikeness and convexity.

scholarly journals New Family of Multivalent Analytic Functions Defined on Complex Hilbert Space

2020 ◽  
pp. 155-165 ◽  
Author(s):  
Abbas Kareem Wanas ◽  
S. R. Swamy
Keyword(s):  
Hilbert Space ◽  
Analytic Functions ◽  
Convex Set ◽  
Extreme Points ◽  
Complex Hilbert Space ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
New Class ◽  
New Family

In this article, we define a certain new class of multivalent analytic functions with negative coefficients on complex Hilbert space. We derive a number of important geometric properties, such as, coefficient estimates, radii of starlikeness and convexity, extreme points and convex set.

scholarly journals A note on d-symmetric operators

1981 ◽  
Vol 23 (3) ◽  
pp. 471-475
Author(s):  
B. C. Gupta ◽  
P. B. Ramanujan
Keyword(s):  
Hilbert Space ◽  
Symmetric Operator ◽  
Compact Operators ◽  
Complex Hilbert Space ◽  
Commutator Ideal ◽  
Derivation Operator ◽  
Double Commutant ◽  
Symmetric Operators ◽  
The Ideal

An operator T on a complex Hilbert space is d-symmetric if , where is the uniform closure of the range of the derivation operator δT(X)=TX−XT. It is shown that if the commutator ideal of the inclusion algebra for a d-symmetric operator is the ideal of all compact operators then T has countable spectrum and T is a quasidiagonal operator. It is also shown that if for a d-symmetric operator I(T) is the double commutant of T then T is diagonal.

scholarly journals Spectral properties of square hyponormal operators

Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 4845-4854
Author(s):  
Muneo Chō ◽  
Dijana Mosic ◽  
Biljana Nacevska-Nastovska ◽  
Taiga Saito
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Bounded Linear Operator ◽  
Spectral Properties ◽  
Complex Hilbert Space ◽  
Hyponormal Operator ◽  
Bounded Linear ◽  
Basic Properties ◽  
Hyponormal Operators ◽  
Eigen Values

In this paper, we introduce a square hyponormal operator as a bounded linear operator T on a complex Hilbert space H such that T2 is a hyponormal operator, and we investigate some basic properties of this operator. Under the hypothesis ?(T) ? (-?(T)) ? {0}, we study spectral properties of a square hyponormal operator. In particular, we show that if z and w are distinct eigen-values of T and x,y ? H are corresponding eigen-vectors, respectively, then ?x,y? = 0. Also, we define nth hyponormal operators and present some properties of this kind of operators.

Fidelity, sub-fidelity, super-fidelity and their preservers

2015 ◽  
Vol 13 (03) ◽  
pp. 1550027
Author(s):  
Li Wang ◽  
Jinchuan Hou ◽  
Kan He
Keyword(s):  
Hilbert Space ◽  
Unitary Operator ◽  
Convex Set ◽  
Quantum Systems ◽  
Complex Hilbert Space ◽  
Quantum States ◽  
Infinite Dimensional

Sub- and super-fidelity describe respectively the lower and super bound of fidelity of quantum states. In this paper, we obtain several properties of sub- and super-fidelity for both finite- and infinite-dimensional quantum systems. Furthermore, let H be a separable complex Hilbert space and ϕ : 𝒮(H) → 𝒮(H) a map, where 𝒮(H) denotes the convex set of all states on H. We show that, if dim H < ∞, or, if dim H = ∞ and ϕ is surjective, then the following statements are equivalent: (1) ϕ preserves the super-fidelity; (2) ϕ preserves the fidelity; (3) ϕ preserves the sub-fidelity; (4) there exists a unitary or an anti-unitary operator U on H such that ϕ(ρ) = UρU† for all ρ ∈ 𝒮(H).

scholarly journals Spectral properties of p-hyponormal operators

1994 ◽  
Vol 36 (1) ◽  
pp. 117-122 ◽  
Author(s):  
Muneo Chō
Keyword(s):  
Hilbert Space ◽  
Spectral Properties ◽  
Polar Decomposition ◽  
Complex Hilbert Space ◽  
Hyponormal Operator ◽  
Bounded Linear ◽  
Hyponormal Operators

Let ℋ be a complex Hilbert space and B(ℋ) be the algebra of all bounded linear opeators on ℋ. An operator T ∈ B(ℋ) is said to be p-hyponormal if (T*T)p–(TT*)p. If p = 1, T is hyponormal and if p = ½ is semi-hyponormal. It is well known that a p-hyponormal operator is p-hyponormal for q≤p. Hyponormal operators have been studied by many authors. The semi-hyponormal operator was first introduced by D. Xia in [7]. The p-hyponormal operators have been studied by A. Aluthge in [1]. Let T be a p-hyponormal operator and T=U|T| be a polar decomposition of T. If U is unitary, Aluthge in [1] proved the following properties.

scholarly journals Spectral properties of n-normal operators

Filomat ◽  
2018 ◽  
Vol 32 (14) ◽  
pp. 5063-5069 ◽  
Author(s):  
Muneo Chō ◽  
Biljana Nacevska
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Spectral Properties ◽  
Normal Operator ◽  
Complex Hilbert Space ◽  
Bounded Linear ◽  
Reducing Subspace ◽  
Normal Operators ◽  
Isolated Point ◽  
Zero Number

For a bounded linear operator T on a complex Hilbert space and n ? N, T is said to be n-normal if T*Tn = TnT*. In this paper we show that if T is a 2-normal operator and satisfies ?(T) ? (-?(T)) ? {0}, then T is isoloid and ?(T) = ?a(T). Under the same assumption, we show that if z and w are distinct eigenvalues of T, then ker(T-z)? ker(T-w). And if non-zero number z ? C is an isolated point of ?(T), then we show that ker(T-z) is a reducing subspace for T. We show that if T is a 2-normal operator satisfying ?(T) ?(-?(T)) = 0, then Weyl?s theorem holds for T. Similarly, we show spectral properties of n-normal operators under similar assumption. Finally, we introduce (n,m)-normal operators and show some properties of this kind of operators.

scholarly journals On [m,C]-isometric operators

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 2073-2080 ◽  
Author(s):  
Muneo Chō ◽  
Ji Lee ◽  
Haruna Motoyoshi
Keyword(s):  
Hilbert Space ◽  
Tensor Product ◽  
Spectral Properties ◽  
Short Proof ◽  
Complex Hilbert Space ◽  
Isometric Operator ◽  
Nilpotent Operator

In this paper we introduce an [m;C]-isometric operator T on a complex Hilbert space H and study its spectral properties. We show that if T is an [m,C]-isometric operator and N is an n-nilpotent operator, respectively, then T + N is an [m + 2n ? 2,C]-isometric operator. Finally we give a short proof of Duggal?s result for tensor product of m-isometries and give a similar result for [m,C]-isometric operators.

scholarly journals Local Spectral Properties Under Conjugations

2021 ◽  
Vol 18 (3) ◽  
Author(s):  
Pietro Aiena ◽  
Fabio Burderi ◽  
Salvatore Triolo
Keyword(s):  
Hilbert Space ◽  
Spectral Properties ◽  
Operator Matrices ◽  
Weyl Type Theorems ◽  
Triangular Operator ◽  
Analytic Core ◽  
Complex Symmetric ◽  
Symmetric Operators ◽  
The Relationship

AbstractIn this paper, we study some local spectral properties of operators having form JTJ, where J is a conjugation on a Hilbert space H and $$T\in L(H)$$ T ∈ L ( H ) . We also study the relationship between the quasi-nilpotent part of the adjoint $$T^*$$ T ∗ and the analytic core K(T) in the case of decomposable complex symmetric operators. In the last part we consider Weyl type theorems for triangular operator matrices for which one of the entries has form JTJ, or has form $$JT^*J$$ J T ∗ J . The theory is exemplified in some concrete cases.

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