Semigroups of operators and an application to spectral theory

1984 ◽  
Vol 96 (1) ◽  
pp. 143-149 ◽  
Author(s):  
W. Ricker
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Spectral Theory ◽  
Continuous Linear Operator ◽  
Integral Transforms ◽  
Fundamental Importance ◽  
Semigroups Of Operators ◽  
Continuous Linear ◽  
Scalar Type

A problem of fundamental importance in Spectral Theory consists of finding criteria for an operator to be of scalar-type in the sense of N. Dunford [1]. One relatively general approach in determining such criteria is based on the method of integral transforms (see for example [4], [5], [6], [11], [12]). For example, if X is a Banach space and T is a continuous linear operator on X, then the group {eitT; t real} exists. As noted by several authors (e.g. [4], [6]), this group can then be effectively used for analysing the operator T.

scholarly journals Semi-embeddings of Banach spaces which are hereditarily c0

1983 ◽  
Vol 26 (2) ◽  
pp. 163-167 ◽  
Author(s):  
L. Drewnowski
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Vector Space ◽  
Unit Ball ◽  
Banach Spaces ◽  
Continuous Linear Operator ◽  
Closed Unit Ball ◽  
Continuous Linear ◽  
Scattered Space ◽  
Complete Set

Following Lotz, Peck and Porta [9], a continuous linear operator from one Banach space into another is called a semi-embedding if it is one-to-one and maps the closed unit ball of the domain onto a closed (hence complete) set. (Below we shall allow the codomain to be an F-space, i.e., a complete metrisable topological vector space.) One of the main results established in [9] is that if X is a compact scattered space, then every semi-embedding of C(X) into another Banach space is an isomorphism ([9], Main Theorem, (a)⇒(b)).

scholarly journals On the spectrum of ψ-contracting operators

2001 ◽  
Vol 14 (3) ◽  
pp. 303-308 ◽  
Author(s):  
Anwar A. Al-Nayef
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Hausdorff Measure ◽  
Measure Of Noncompactness ◽  
Continuous Linear Operator ◽  
Continuous Linear ◽  
Hausdorff Measure Of Noncompactness

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.

scholarly journals On totally paranormal operators

2002 ◽  
Vol 66 (3) ◽  
pp. 425-441 ◽  
Author(s):  
Christoph Schmoeger
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Continuous Linear Operator ◽  
Complex Banach Space ◽  
Weyl’S Theorem ◽  
Continuous Linear ◽  
Spectral Mapping Theorem ◽  
Spectral Mapping ◽  
Operator Equations ◽  
Weyl Spectrum

A continuous linear operator on a complex Banach space is said to be paranormal if ‖Tx‖2 ≤ ‖T2x‖ ‖x‖ for all x ∈ X. T is called totally paranormal if T–λ is paranormal for every λ ∈ C. In this paper we investigate the class of totally paranormal operators. We shall see that Weyl's theorem holds for operators in this class. We also show that for totally paranormal operators the Weyl spectrum satisfies the spectral mapping theorem. In Section 5 of this paper we investigate the operator equations eT = eS and eTeS = eSeT for totally paranormal operators T and S.

scholarly journals OPERATORS ON C0(L,X) WHOSE RANGE DOES NOT CONTAIN c0

2008 ◽  
Vol 77 (3) ◽  
pp. 515-520
Author(s):  
JARNO TALPONEN
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Banach Spaces ◽  
Hausdorff Space ◽  
Continuous Linear Operator ◽  
Continuous Linear ◽  
Locally Compact ◽  
Weakly Compact ◽  
Isolated Points ◽  
Locally Compact Hausdorff Space

AbstractThis paper contains two results: (a) if $\mathrm {X}\neq \{0\}$ is a Banach space and (L,τ) is a nonempty locally compact Hausdorff space without isolated points, then each linear operator T:C0(L,X)→C0(L,X) whose range does not contain an isomorphic copy of c00 satisfies the Daugavet equality $\|\mathbf {I}+T\|=1+\|T\|$; (b) if Γ is a nonempty set and X and Y are Banach spaces such that X is reflexive and Y does not contain c0 isomorphically, then any continuous linear operator T:c0(Γ,X)→Y is weakly compact.

scholarly journals Linear operators whose domain is locally convex

1977 ◽  
Vol 20 (4) ◽  
pp. 293-299 ◽  
Author(s):  
N. J. Kalton
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Vector Space ◽  
Unit Ball ◽  
Topological Vector Space ◽  
Continuous Linear Operator ◽  
Linear Operators ◽  
Continuous Linear ◽  
Locally Convex

Let F be an arbitrary topological vector space; we shall say that a subset S of F is quasi-convex if the set of continuous affine functionals on S separates the points of S. If X is a Banach space and T : X → F is a continuous linear operator, then T is quasi-convex if is quasi-convex, where U is the unit ball of X.

EXOTIC LAPLACIANS AND DERIVATIVES OF WHITE NOISE

2011 ◽  
Vol 14 (01) ◽  
pp. 1-14 ◽  
Author(s):  
LUIGI ACCARDI ◽  
UN CIG JI ◽  
KIMIAKI SAITÔ
Keyword(s):  
Linear Operator ◽  
White Noise ◽  
Continuous Linear Operator ◽  
Higher Order ◽  
Continuous Linear ◽  
White Noise Functionals ◽  
Derivatives Of

In this paper, we give a relationship between the exotic Laplacians and the Lévy Laplacians in terms of the higher-order derivatives of white noise by introducing a bijective and continuous linear operator acting on white noise functionals. Moreover, we study a relationship between exotic Laplacians, acting on higher-order singular functionals, each other in terms of the constructed operator.

scholarly journals A note on Dunford-Pettis operators

1987 ◽  
Vol 29 (2) ◽  
pp. 271-273 ◽  
Author(s):  
J. R. Holub
Keyword(s):  
Linear Operator ◽  
Positive Operator ◽  
Continuous Linear Operator ◽  
Positive Operators ◽  
Regular Operator ◽  
Continuous Linear

Talagrand has shown [4, p. 76] that there exists a continuous linear operator from L1[0, 1] to c0 which is not a Dunford-Pettis operator. In contrast to this result, Gretsky and Ostroy [2] have recently proved that every positive operator from L[0, 1] to c0 is a Dunford-Pettis operator, hence that every regular operator between these spaces (i.e. a difference of positive operators) is Dunford-Pettis.

Linearization of a Contractive Homeomorphism

1968 ◽  
Vol 20 ◽  
pp. 1387-1390
Author(s):  
Ludvik Janos
Keyword(s):  
Linear Operator ◽  
Topological Space ◽  
Vector Space ◽  
Topological Vector Space ◽  
Continuous Linear Operator ◽  
Continuous Linear ◽  
Topological Embedding

Let X be a topological space and ϕ: X ⟶ X a continuous self-mapping of X. We say that ϕ is linearized in L by Φ if there exists a topological embedding μ: X ⟶ L of the space X into the linear topological vector space L such that for all x ϵ X, μ (ϕ (x)) = Φ (μ (x)), where ϕ is a continuous linear operator on L.

Bounded continuous linear operator on cone normed space C'[a,b] to C[a,b]

2016 ◽  
Vol 5 ◽  
pp. 65-73
Author(s):  
Sunarsini ◽  
Sadjidon ◽  
Agus Nur Ahmad Syarifudin
Keyword(s):  
Linear Operator ◽  
Normed Space ◽  
Continuous Linear Operator ◽  
Continuous Linear

scholarly journals Sufficient conditions for a continuous linear operator to be weakly compact

1972 ◽  
Vol 7 (2) ◽  
pp. 183-190 ◽  
Author(s):  
Joe Howard ◽  
Kenneth Melendez
Keyword(s):  
Linear Operator ◽  
Sufficient Conditions ◽  
Continuous Linear Operator ◽  
Continuous Operator ◽  
Continuous Linear ◽  
Weakly Compact ◽  
Completely Continuous ◽  
Completely Continuous Operator ◽  
Locally Convex

A locally convex topological vector (LCTV) space E is said to have property V (Dieudonné property) if for every complete separated LCTV space F, every unconditionally converging (weakly completely continuous) operator T: E → F is wsakly compact. First, an investigation of the permanence of property V is given. The permanence of the Dieudonné is analogous. Relationships between property V and the Dieudonné property are then given.

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