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1.
Let T be an M-hyponormal operator acting on infinite dimensional separable Hilbert space and let
be the Riesz idempotent for λ0, where D is a closed disk of center λ0 which contains no other points of σ (T). In this note we show that E is self-adjoint and
As an application, if T is an algebraically M-hyponormal operator then we prove : (i) Weyl’s theorem holds for f(T) for every
(ii) a-Browder’s theorem holds for f(S) for every
and f ∈ H(σ(S)); (iii) the the spectral mapping theorem holds for the Weyl spectrum of T and for the essential approximate point spectrum of T. 相似文献
2.
Let T be a w-hyponormal operator on a Hilbert space H,
its Aluthge transform, λ an isolated point of the spectrum of T, and Eλ and
the Riesz idempotents, with respect to λ, of T and
respectively. It is shown that
Consequently, Eλ is self-adjoint,
and
if λ ≠ 0. Moreover, it is shown that Weyl’s theorem holds for f(T), where f ∈ H(σ (T)). 相似文献
3.
Given a continuous linear operator T L(x) defined on a separable
-space X, we will show that T satisfies the Hypercyclicity Criterion if and only if for any strictly increasing sequence of positive integers
such that
the sequence
is hypercyclic. In contrast we will also prove that, for any hypercyclic vector x X of T, there exists a strictly increasing sequence
such that
and
is somewhere dense, but not dense in X. That is, T and
do not share the same hypercyclic vectors. 相似文献
4.
Pei Yuan Wu 《Integral Equations and Operator Theory》2006,56(4):559-569
Let A be a bounded linear operator on a complex separable Hilbert space H. We show that A is a C0(N) contraction if and only if
, where U is a singular unitary operator with multiplicity
and x1, . . . , xd are orthonormal vectors satisfying
. For a C0(N) contraction, this gives a complete characterization of its polar decompositions with unitary factors. 相似文献
5.
Henrik Petersson 《Integral Equations and Operator Theory》2007,57(3):413-423
We prove that for any weighted backward shift B = Bw on an infinite dimensional separable Hilbert space H whose weight sequence w = (wn) satisfies
, the conjugate operator
is hypercyclic on the space S(H) of self-adjoint operators on H provided with the topology of uniform convergence on compact sets. That is, there exists an
such that
is dense in S(H). We generalize the result to more general conjugate maps
, and establish similar results for other operator classes in the algebra B(H) of bounded operators, such as the ideals K(H) and N(H) of compact and nuclear operators respectively. 相似文献
6.
Maribel Loaiza 《Integral Equations and Operator Theory》2005,51(1):141-153
Let
and
be a finite collection of smooth curves in D. Given k points
consider the family
of all bounded and continuous functions on
with finite limits at
and radial limits at zk. We study the Toeplitz operator algebra
corresponding to Mr and we prove that its Calkin algebra is isomorphic to the algebra of all continuous functions on some compact set. This fact implies that the commutator of two Toeplitz operators with this kind of symbols is compact. We also prove that the semi-commutator of such Toeplitz operators is not compact, in general. 相似文献
7.
Onur Yavuz 《Integral Equations and Operator Theory》2007,58(3):433-446
We consider a multiply connected domain
where
denotes the unit disk and
denotes the closed disk centered at
with radius r
j
for j = 1, . . . , n. We show that if T is a bounded linear operator on a Banach space X whose spectrum contains ∂Ω and does not contain the points λ1, λ2, . . . , λ
n
, and the operators T and r
j
(T − λ
j
I)−1 are polynomially bounded, then there exists a nontrivial common invariant subspace for T
* and (T − λ
j
I)*-1. 相似文献
8.
Egor A. Alekhno 《Positivity》2009,13(1):3-20
Let T be a positive operator on a Banach lattice E. Some properties of Weyl essential spectrum σew(T), in particular, the equality , where is the set of all compact operators on E, are established. If r(T) does not belong to Fredholm essential spectrum σef(T), then for every a ≠ 0, where T−1 is a residue of the resolvent R(., T) at r(T). The new conditions for which implies , are derived. The question when the relation holds, where is Lozanovsky’s essential spectrum, will be considered. Lozanovsky’s order essential spectrum is introduced. A number of
auxiliary results are proved. Among them the following generalization of Nikol’sky’s theorem: if T is an operator of index zero, then T = R + K, where R is invertible, K ≥ 0 is of finite rank. Under the natural assumptions (one of them is ) a theorem about the Frobenius normal form is proved: there exist T-invariant bands such that if
, where , then an operator on Di is band irreducible.
相似文献
9.
Let
be a C*-algebra and X a Hilbert C*
-module. If
is a projection, let
be the p-sphere of X. For φ a state of
with support p in
and
consider the modular vector state φx of
given by
The spheres
provide fibrations
and
These fibrations enable us to examine the homotopy type of the sets of modular vector states, and relate it to the homotopy type of unitary groups and spaces of projections. We regard modular vector states as generalizations of pure states to the context of Hilbert C*-modules, and the above fibrations as generalizations of the projective fibration of a Hilbert space. 相似文献
10.
11.
On the Range of the Aluthge Transform 总被引:1,自引:0,他引:1
Let
be the algebra of all bounded linear operators on a complex separable Hilbert space
For an operator
let
be the Aluthge transform of T and we define
for all
where T = U|T| is a polar decomposition of T. In this short note, we consider an elementary property of the range
of Δ. We prove that R(Δ) is neither closed nor dense in
However R(Δ) is strongly dense if
is infinite dimensional.
An erratum to this article is available at . 相似文献
12.
Disjointness Preserving Operators on Complex Riesz Spaces 总被引:2,自引:0,他引:2
It is proven that ifE
and F
are complex Riesz spaces and ifT is an order bounded disjointness preserving operator fromE
intoF
, then
This fundamental result of M. Meyer is obtained by elementary means using as the main tool the functional calculus derived from the Freudenthal spectral theorem. It is also shown that ifT is an order bounded disjointness preserving operator, a formula of the form
holds. It implies a polar decomposition of an order bounded disjointness preserving operator as the product of a Riesz homomorphism and an orthomorphism. Results of P. Meyer-Nieberg in this regard are generalized. 相似文献
13.
Let Q(x, y) = 0 be an hyperbola in the plane. Given real numbers β ≡ β (2n)={ β ij } i,j ≥ 0,i+j ≤ 2n , with β00 > 0, the truncated Q-hyperbolic moment problem for β entails finding necessary and sufficient conditions for the existence of a positive Borel measure μ, supported in Q(x, y) = 0, such that
We prove that β admits a Q-representing measure μ (as above) if and only if the associated moment matrix
is positive semidefinite, recursively generated, has a column relation Q(X,Y) = 0, and the algebraic variety
associated to β satisfies card
In this case,
if
then β admits a rank
-atomic (minimal) Q-representing measure; if
then β admits a Q-representing measure μ satisfying
相似文献
14.
15.
The C*-algebra
generated by the Bergman and anti-Bergman projections and by the operators of multiplication by piecewise continuous functions on the Lebesgue space L2(Π) over the upper half-plane is studied. Making use of a local principle, limit operators techniques, and the Plamenevsky results on two-dimensional singular integral operators with coefficients admitting homogeneous discontinuities we reduce the study to simpler C*-algebras associated with points
and pairs
We construct a symbol calculus for unital C*-algebras generated by n orthogonal projections sum of which equals the unit and by m one-dimensional orthogonal projections. Such algebras are models of local algebras at points z ∈∂Π being the discontinuity points of coefficients. A symbol calculus for the C*- algebra
and a Fredholm criterion for the operators
are obtained. Finally, a C*-algebra isomorphism between the quotient algebra
where
is the ideal of compact operators, and its analogue
for the unit disk is constructed. 相似文献
16.
Consider the Schrödinger operator
with a complex-valued
potential v of period
Let
and
be the eigenvalues of L that are close to
respectively, with periodic (for n even),
antiperiodic (for n odd), and Dirichelet
boundary conditions on [0,1], and let
be the diameter of the spectral
triangle with vertices
We prove the following statement: If
then v(x) is a Gevrey function, and moreover
相似文献
17.
Some Properties of Essential Spectra of a Positive Operator 总被引:1,自引:1,他引:0
Egor A. Alekhno 《Positivity》2007,11(3):375-386
Let E be a Banach lattice, T be a bounded operator on E. The Weyl essential spectrum σew(T) of the operator T is a set
, where
is a set of all compact operators on E. In particular for a positive operator T next subsets of the spectrum
are introduced in the article. The conditions by which
implies either
or
are investigated, where σef(T) is the Fredholm essential spectrum. By this reason, the relations between coefficients of the main part of the Laurent series
of the resolvent R(., T) of a positive operator T around of the point λ = r(T) are studied. The example of a positive integral operator T : L1→ L∞ which doesn’t dominate a non-zero compact operator, is adduced. Applications of results which are obtained, to the spectral
theory of band irreducible operators, are given. Namely, the criteria when the operator inequalities 0 ≤ S < T imply the spectral radius inequality r(S) < r(T), are established, where T is a band irreducible abstract integral operator. 相似文献
18.
In this note we give an example of an ∞-hyponormal operator T whose Aluthge transform
is not (1+ɛ)-hyponormal for any ɛ > 0 and show that the sequence
of interated Aluthge transforms of T need not converge in the weak operator topology, which solve two problems in [6]. 相似文献
19.
Marilyn Breen 《Aequationes Mathematicae》2004,67(3):263-275
Summary.
We establish the following Helly-type result for infinite families
of starshaped sets in
Define the function f on
{1, 2} by
f(1) = 4,
f(2) = 3.
Let
be a fixed positive number, and let
be a uniformly bounded family of compact sets
in the plane. For k = 1, 2, if every
f(k)
(not necessarily distinct) members of
intersect in a starshaped set whose
kernel contains a k-dimensional
neighborhood of radius
, then
is a starshaped set whose kernel is at least
k-dimensional.
The number f(k) is best in each case.
In addition, we present a few results concerning the dimension of
the kernel in an intersection of starshaped sets in
Some of these involve finite families of sets, while others
involve infinite families and make use of the Hausdorff metric. 相似文献
20.
Takuya Mine 《Annales Henri Poincare》2005,6(1):125-154
We study the spectral properties of a two-dimensional magnetic Schrödinger operator
The magnetic field is given by
where B > 0 is a constant,
and the points
are uniformly separated. We give an upper bound for the number of eigenvalues of HN between two Landau levels or below the lowest Landau level, when N is finite. We prove the spectral localization of HN near the spectrum of the single solenoid operator, when
are far from each other, all the values
are the same, and the boundary conditions at zj are uniform. We determine the deficiency indices of the minimal operator and give a characterization of self-adjoint extensions of the minimal operator.submitted 28/05/04, accepted 23/07/04 相似文献