decomposable operator
Recently Published Documents


TOTAL DOCUMENTS

10
(FIVE YEARS 0)

H-INDEX

3
(FIVE YEARS 0)

2019 ◽  
Vol 82 (1) ◽  
pp. 79-113
Author(s):  
M.I. Stessin ◽  
A.B. Tchernev

2010 ◽  
Vol 62 (2) ◽  
pp. 305-319
Author(s):  
He Hua ◽  
Dong Yunbai ◽  
Guo Xianzhou

AbstractLet 𝓗 be a complex separable Hilbert space and ℒ(𝓗) denote the collection of bounded linear operators on 𝓗. In this paper, we show that for any operator A ∈ ℒ(𝓗), there exists a stably finitely (SI) decomposable operator A∈, such that ‖A−A∈‖ 𝓗 ∈ andA′(A∈)/ rad A′(A∈) is commutative, where rad A′(A∈) is the Jacobson radical of A′(A∈). Moreover, we give a similarity classification of the stably finitely decomposable operators that generalizes the result on similarity classification of Cowen–Douglas operators given by C. L. Jiang.


1996 ◽  
Vol 38 (1) ◽  
pp. 21-28 ◽  
Author(s):  
T. L. Miller ◽  
V. G. Miller

AbstractA Banach space operator has property (δ) if and only if it is the quotient of a decomposable operator, equivalently, if and only if its adjoint has Bishop's property (β). Within this class of operators, it is shown that quasisimilarity preserves essential spectra.


1992 ◽  
Vol 34 (1) ◽  
pp. 109-116
Author(s):  
Ridgley Lange ◽  
Shengwang Wang

In this note we characterize certain types of spectral decomposition in terms of “universal” notions valid for any operator on a Banach space. To be precise, let X be a complex Banach space and let T be a bounded linear operator on X. If F is a closed set in the plane C, let X(T, F) consist of all y ∈ X satisfying thes identitywhere f:C\F → X is analytic. It is then easy to see that X(T, F) is a T-invariant linear manifold in X. Moreover, if y ∈ X thenis a compact subset of the spectrum σ(T). Our aim is to give necessary and sufficient conditions for a decomposable or strongly decomposable operator in terms of X(T, F) and γ(y, T). Recall that T is decomposable if whenever G1G2 are open and cover C there exist T-invariant closed linear manifolds M1, M2 with X= M1 + M2 and σ(T | M1) ⊂ Gi(i = 1,2) (equivalently, σ(T | Mi)⊂ Ḡi, see [4, p. 57]). In this case, X(T, F) is norm closed if Fis closed and each y in X has a unique maximally defined local resolvent satisfying (1.1) on C\Fy; Fy is called the local spectrum σ(y, T) and coincides with γ(y, T). Hence T has the single valued extension property (SVEP); i.e., zero is the only analytic function f:V → X satisfying (z − T)f(z) = 0 on V. If T is decomposable and the restriction T | X(T, F) is also decomposable for each closed F, then T is called strongly decomposable. We point out that Albrecht [2] has shown by example that not every decomposable operator is strongly decomposable, while Eschmeier [6]has given a simpler construction to show that this phenomenon occurs even in Hilbert space.


1988 ◽  
Vol 30 (3) ◽  
pp. 249-257
Author(s):  
Ridgley Lange ◽  
Shengwang Wang

It is now well-known that decomposable operators have a rich structure theory; in particular, an operator is decomposable iff its adjoint is [3]. There are many other criteria for decomposability [8], [9]. In Theorem 2.2 of this paper (see below) we give several new ones. Some of these (e.g. (ii), (iii)) are “relaxations” of conditions given in [7] and [8]. Assertion (vi) is a version of a result in [10]. Characterizations (iv)and (v) are novel in two respects. For instance, (v) states that an operator Tcan be “patched” together into a decomposable operator if it has an invariant subspace Y such that T | Y and the coinduced operator T | Y are both decomposable. Secondly, in this way the strongly analytic subspace appears in the theory of spectral decomposition.


1987 ◽  
Vol 31 (3) ◽  
pp. 438-445 ◽  
Author(s):  
Ridgley Lange ◽  
Shengwang Wang

1980 ◽  
Vol 21 (1) ◽  
pp. 69-70 ◽  
Author(s):  
Ridgley Lange

In [3] E. Bishop introduced the notion of an operator with a “duality theory of type 3” and gave a certain sufficient condition for an operator to have a duality theory of type 3. In this note we show that in fact Bishop's sufficient condition implies that a given operator is decomposable [4]. Moreover, this condition characterizes a decomposable operator.


1975 ◽  
Vol 27 (3) ◽  
pp. 725-735 ◽  
Author(s):  
M. Radjabalipour ◽  
H. Radjavi

The main purpose of this paper is to show that a bounded Hilbert-space operator whose imaginary part is in the Schatten class Cp(1 ≦ p < ∞ ) is strongly decomposable. This answers affirmatively a question raised by Colojoara and Foias [6, Section 5(e), p. 218].In case 0 ≦ T* — T ∈ C1, it was shown by B. Sz.-Nagy and C. Foias [2, p. 442; 25, p. 337] that T has many properties analogous to those of a decomposable operator and by A. Jafarian [11] that T is strongly decomposable. The authors of [11] and [24] employ the properties of the characteristic function of the contraction operator obtained from the Cayley transform of T;


Sign in / Sign up

Export Citation Format

Share Document