scholarly journals Nonlinear Isometries on Schatten-pClass in Atomic Nest Algebras

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Kan He ◽  
Qing Yuan
Keyword(s):  
Hilbert Space ◽  
Complete Characterization ◽  
Complex Hilbert Space ◽  
Nest Algebra ◽  
Nest Algebras ◽  
Surjective Isometry

LetHbe a complex Hilbert space; denote by Alg 𝒩and𝒞p(H)the atomic nest algebra associated with the atomic nest𝒩onHand the space of Schatten-pclass operators on,Hrespectively. Let𝒞p(H)∩Alg 𝒩be the space of Schatten-pclass operators in Alg 𝒩. When1≤p<+∞andp≠2, we give a complete characterization of nonlinear surjective isometries on𝒞p(H)∩Alg 𝒩. Ifp=2, we also prove that a nonlinear surjective isometry on𝒞2(H)∩Alg 𝒩is the translation of an orthogonality preserving map.

Generators of Nest Algebras

1974 ◽  
Vol 26 (3) ◽  
pp. 565-575 ◽  
Author(s):  
W. E. Longstaff
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Linear Operators ◽  
Nest Algebra ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Closed Algebra ◽  
Nest Algebras ◽  
Weakly Closed

A collection of subspaces of a Hilbert space is called a nest if it is totally ordered by inclusion. The set of all bounded linear operators leaving invariant each member of a given nest forms a weakly-closed algebra, called a nest algebra. Nest algebras were introduced by J. R. Ringrose in [9]. The present paper is concerned with generating nest algebras as weakly-closed algebras, and in particular with the following question which was first raised by H. Radjavi and P. Rosenthal in [8], viz: Is every nest algebra on a separable Hilbert space generated, as a weakly-closed algebra, by two operators? That the answer to this question is affirmative is proved by first reducing the problem using the main result of [8] and then by using a characterization of nests due to J. A. Erdos [2].

scholarly journals Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras

2011 ◽  
Vol 2011 ◽  
pp. 1-6
Author(s):  
Dangui Yan ◽  
Chengchang Zhang
Keyword(s):  
Hilbert Space ◽  
Closed Subspace ◽  
Complex Hilbert Space ◽  
Generalized Derivations ◽  
Nest Algebra ◽  
Bounded Operators ◽  
Subspace Lattice ◽  
Nest Algebras

LetHbe a complex Hilbert space andB(H)the collection of all linear bounded operators,Ais the closed subspace lattice including 0 anH, thenAis a nest, accordingly algA={T∈B(H):TN⊆N,  ∀N∈A}is a nest algebra. It will be shown that of nest algebra, generalized derivations are generalized inner derivations, and bilocal Jordan derivations are inner derivations.

scholarly journals Lyapunov Type Theorems for Exponential Stability of Linear Skew-Product Three-Parameter Semiflows with Discrete Time

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 47 ◽  
Author(s):  
Davor Dragičević ◽  
Ciprian Preda
Keyword(s):  
Hilbert Space ◽  
Exponential Stability ◽  
Discrete Time ◽  
Lyapunov Functions ◽  
Complete Characterization ◽  
Skew Product ◽  
Linear Perturbations

For linear skew-product three-parameter semiflows with discrete time acting on an arbitrary Hilbert space, we obtain a complete characterization of exponential stability in terms of the existence of appropriate Lyapunov functions. As a nontrivial application of our work, we prove that the notion of an exponential stability persists under sufficiently small linear perturbations.

Perturbation of a nest algebra module

1983 ◽  
Vol 93 (2) ◽  
pp. 303-306 ◽  
Author(s):  
Sotirios Karanasios
Keyword(s):  
General Situation ◽  
Compact Perturbation ◽  
Nest Algebra ◽  
Nest Algebras ◽  
Weakly Closed ◽  
Carry Over ◽  
Algebra Module ◽  
Algebra Of Operators

Fall, Arveson and Muhly(4) characterized the compact perturbation of nest algebras. In fact they proved that the compact perturbation of a nest algebra corresponding to a nest of projections is the algebra of operators which are quasitriangular relative to this nest. Erdos and Power(3) investigated weakly closed ideals and modules of nest algebras and these exhibit properties that are very close to the properties of the nest algebras themselves. They also showed that in certain cases, as in the case when the homomorphism which determines the nest algebra module is continuous, the results of Fall, Arveson and Muhly carry over to the more general situation. In this paper we provide a characterization of the compact perturbation of any nest algebra module.

scholarly journals Isometries of Hilbert space valued function spaces

1996 ◽  
Vol 61 (2) ◽  
pp. 150-161 ◽  
Author(s):  
Beata Randrianantoanina
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Invariant Function ◽  
Function Spaces ◽  
Measurable Operator ◽  
Complex Rearrangement ◽  
Rearrangement Invariant Function Spaces ◽  
Surjective Isometry ◽  
Almost All

AbstractLet X be a (real or complex) rearrangement-invariant function space on Ω (where Ω = [0, 1] or Ω ⊆ N) whose norm is not proportional to the L2-norm. Let H be a separable Hilbert space. We characterize surjective isometries of X (H). We prove that if T is such an isometry then there exist Borel maps a: Ω → + K and σ: Ω → Ω and a strongly measurable operator map S of Ω into B (H) so that for almost all ω, S(ω) is a surjective isometry of H, and for any f ∈ X(H), T f(ω) = a(ω)S(ω)(f(σ(ω))) a.e. As a consequence we obtain a new proof of the characterization of surjective isometries in complex rearrangement-invariant function spaces.

scholarly journals Antinormal composition operators on $ \mbf{\ell^2}$

2008 ◽  
Vol 39 (4) ◽  
pp. 347-352 ◽  
Author(s):  
Gyan Prakash Tripathi ◽  
Nand Lal
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Bounded Linear Operator ◽  
Composition Operators ◽  
Complete Characterization ◽  
Inner Product ◽  
Complex Numbers ◽  
Bounded Linear ◽  
Normal Operators

A bounded linear operator $ T $ on a Hilbert space $ H $ is called antinormal if the distance of $ T $ from the set of all normal operators is equal to norm of $ T $. In this paper, we give a complete characterization of antinormal composition operators on $ \ell^2 $, where $ \ell^2 $ is the Hilbert space of all square summable sequences of complex numbers under standard inner product on it.

Successions of J-bessel in Spaces with Indefinite Metric

2021 ◽  
Vol 20 ◽  
pp. 144-151
Author(s):  
Osmin Ferrer ◽  
Luis Lazaro ◽  
Jorge Rodriguez
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Complete Characterization ◽  
Indefinite Metric ◽  
Krein Spaces ◽  
Definition Of

A definition of Bessel’s sequences in spaces with an indefinite metric is introduced as a generalization of Bessel’s sequences in Hilbert spaces. Moreover, a complete characterization of Bessel’s sequences in the Hilbert space associated to a space with an indefinite metric is given. The fundamental tools of Bessel’s sequences theory are described in the formalism of spaces with an indefinite metric. It is shown how to construct a Bessel’s sequences in spaces with an indefinite metric starting from a pair of Hilbert spaces, a condition is given to decompose a Bessel’s sequences into in spaces with an indefinite metric so that this decomposition generates a pair of Bessel’s sequences for the Hilbert spaces corresponding to the fundamental decomposition. In spaces where there was no norm, it seemed impossible to construct Bessel’s sequences. The fact that in [1] frame were constructed for Krein spaces motivated us to construct Bessel’s sequences for spaces of indefinite metric.

scholarly journals A characterization of spectral operators on Hilbert spaces

1982 ◽  
Vol 23 (1) ◽  
pp. 91-95 ◽  
Author(s):  
Ernst Albrecht
Keyword(s):  
Hilbert Space ◽  
Banach Algebra ◽  
Essential Spectrum ◽  
Hilbert Spaces ◽  
Complex Hilbert Space ◽  
Linear Operators ◽  
Spectral Operator ◽  
Bounded Linear ◽  
Image Position

Let H be a complex Hilbert space and denote by B(H) the Banach algebra of all bounded linear operators on H. In [5; 6] J. Ph. Labrousse proved that every operator S∈B(H) which is spectral in the sense of N. Dunford (see [3]) is similar to a T∈B(H) with the following propertyConversely, he showed that given an operator S∈B(H) such that its essential spectrum (in the sense of [5; 6]) consists of at most one point and such that S is similar to a T∈B(H) with the property (1), then S is a spectral operator. This led him to the conjecture that an operator S∈B(H) is spectral if and only if it is similar to a T∈B(H) with property (1). The purpose of this note is to prove this conjecture in the case of operators which are decomposable in the sense of C. Foias (see [2]).

Experimental Characterization of Mechanical Behavior of Cord-Rubber Composites

1982 ◽  
Vol 10 (1) ◽  
pp. 37-54 ◽  
Author(s):  
M. Kumar ◽  
C. W. Bert
Keyword(s):  
Response Characteristic ◽  
Cord Compression ◽  
Complete Characterization ◽  
Strain Response ◽  
Strain Gages ◽  
Experimental Characterization ◽  
Rubber Composites ◽  
Stress Strain ◽  
Strain Data

Abstract Unidirectional cord-rubber specimens in the form of tensile coupons and sandwich beams were used. Using specimens with the cords oriented at 0°, 45°, and 90° to the loading direction and appropriate data reduction, we were able to obtain complete characterization for the in-plane stress-strain response of single-ply, unidirectional cord-rubber composites. All strains were measured by means of liquid mercury strain gages, for which the nonlinear strain response characteristic was obtained by calibration. Stress-strain data were obtained for the cases of both cord tension and cord compression. Materials investigated were aramid-rubber, polyester-rubber, and steel-rubber.

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