共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
All compact AC(σ) operators have a representation analogous to that for compact normal operators. As a partial converse we obtain conditions
which allow one to construct a large number of such operators. Using the results in the paper, we answer a number of questions
about the decomposition of a compact AC(σ) operator into real and imaginary parts.
相似文献
3.
Some properties and applications of meromorphic factorization of matrix functions are studied. It is shown that a meromorphic
factorization of a matrix function G allows one to characterize the kernel of the Toeplitz operator with symbol G without actually having to previously obtain a Wiener–Hopf factorization. A method to turn a meromorphic factorization into
a Wiener–Hopf one which avoids having to factorize a rational matrix that appears, in general, when each meromorphic factor
is treated separately, is also presented. The results are applied to some classes of matrix functions for which the existence
of a canonical factorization is studied and the factors of a Wiener–Hopf factorization are explicitly determined.
Submitted: April 15, 2007. Revised: October 26, 2007. Accepted: December 12, 2007. 相似文献
4.
Marcus Carlsson 《Integral Equations and Operator Theory》2008,61(4):593-598
In [3], M. J. Cowen and R. G. Douglas prove that the adjoint of a Hilbert space operator T is in the class if and only if T is unitarily equivalent with the operator M
z
on a Hilbert space -valued analytic functions, where M
z
denotes the operator of multiplication by the independent variable. The proof involves holomorphic vector bundles and Grauert’s
theorem.
In this paper we use a theorem by I. Gohberg and L. Rodman [4] to give a more elementary proof of this fact, which also works
for Banach space operators.
相似文献
5.
Stevo Stević 《Mediterranean Journal of Mathematics》2008,5(1):61-76
In this paper we investigate harmonic Hardy-Orlicz and Bergman-Orlicz b
φ,α
(B) spaces, using an identity of Hardy-Stein type. We also extend the notion of the Lusin property by introducing (φ, α)-Lusin property with respect to a Stoltz domain. The main result in the paper is as follows: Let be a nonnegative increasing convex function twice differentiable on (0, ∞), and u a harmonic function on the unit ball B in . Then the following statements are equivalent:
相似文献
(a) | . |
(b) | . |
(c) | u has (φ, α)-Lusin property with respect to a Stoltz domain with half-angle β, for any . |
(d) | u has (φ, α)-Lusin property with respect to a Stoltz domain with half-angle β, for some . |
6.
In this paper, we introduce Xia spectra of n-tuples of operators satisfying |T
2| ≥ U|T
2|U* for the polar decomposition of T = U|T| and we extend Putnam’s inequality to these tuples [7].
This research is partially supported by Grant-in-Aid Research No.17540176. 相似文献
7.
Suppose that is a trigonometric polynomial of the form (z) = Nn=-N an zn. It is well-known that T is normal if and only if | a– N| = | aN| and the Fourier coefficients of satisfy the following symmetry condition:
In this paper we provide a complete criterion for hyponormality of T when satisfies a partial symmetry condition:
相似文献
8.
Fiana Jacobzon Simeon Reich David Shoikhet 《Journal of Fixed Point Theory and Applications》2009,5(1):63-91
We study commutativity and embeddability (into continuous semi-groups) properties of linear fractional self-mappings of the
open unit disk in the complex plane. The common thread in our approach is the classical notion of the Kœnigs function which
we use in each of the three possible cases (dilation, hyperbolic and parabolic). Since we are interested in a classical subject,
the paper is written in the style of a survey, in order to make it accessible to a wider audience. Therefore it contains,
in addition to our new results, an exposition of most relevant facts.
Dedicated to Professor Felix E. Browder with admiration and respect 相似文献
9.
We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space with the resolvent norm
that is constant in a neighbourhood of zero.
相似文献
10.
For real parameters a, b, c, and t, where c is not a nonpositive integer, we determine exactly when the integral operator
is bounded on
where
is the open unit ball in
and dvt (z) = (1 − |z| 2) t dv (z) with dv being volume measure on
The characterization remains the same if we replace (1 − 〈z, w 〉) c in the integral kernel above by its modulus |1 − 〈z, w〉| c. 相似文献
11.
Teresa Bermúdez Isabel Marrero Antonio Martinón 《Integral Equations and Operator Theory》2009,64(4):487-494
A bounded linear operator T on a Hilbert space H is called an m-isometry for a positive integer m if . We prove some properties concerning the behaviour of the orbit of an m-isometry. For example, every orbit of an m-isometry is eventually norm increasing and some m-isometries can not be N-supercyclic, that is, there does not exist an N-dimensional subspace EN such that the orbit of T at EN is dense in H.
To Professor José Rodríguez Expósito on his 60th birthday 相似文献
12.
Dr. Mohammed Hichem Mortad 《Integral Equations and Operator Theory》2009,64(3):399-408
We give a spectral analysis of some unbounded normal product HK of two self-adjoint operators H and K (which appeared in [7]) and we say why it is not self-adjoint even if the spectrum of one of the operators is sufficiently
“asymmetric”. Then, we investigate the self-adjointness of KH (given it is normal) for arbitrary self-adjoint H and K by giving a counterexample and some positive results and hence finishing off with the whole question of normal products of
self-adjoint operators (appearing in [1, 7, 12]).
The author was supported in part by CNEPRU: B01820070020 (Ministry of Higher Education, Algeria). 相似文献
13.
Ilwoo Cho 《Complex Analysis and Operator Theory》2007,1(3):367-398
We identify two noncommutative structures naturally associated with countable directed graphs. They are formulated in the
language of operators on Hilbert spaces. If G is a countable directed graphs with its vertex set V(G) and its edge set E(G), then we associate partial isometries to the edges in E(G) and projections to the vertices in V(G). We construct a corresponding von Neumann algebra
as a groupoid crossed product algebra
of an arbitrary fixed von Neumann algebra M and the graph groupoid
induced by G, via a graph-representation (or a groupoid action) α. Graph groupoids are well-determined (categorial) groupoids. The graph
groupoid
of G has its binary operation, called admissibility. This
has concrete local parts
, for all e ∈ E(G). We characterize
of
, induced by the local parts
of
, for all e ∈ E(G). We then characterize all amalgamated free blocks
of
. They are chracterized by well-known von Neumann algebras: the classical group crossed product algebras
, and certain subalgebras
(M) of operator-valued matricial algebra
. This shows that graph von Neumann algebras identify the key properties of graph groupoids.
Received: December 20, 2006. Revised: March 07, 2007. Accepted: March 13, 2007. 相似文献
14.
S. P. Eveson 《Integral Equations and Operator Theory》2005,53(3):331-341
Given k ∈ L1 (0,1) satisfying certain smoothness and growth conditions at 0, we consider the Volterra convolution operator Vk defined on Lp (0,1) by
and its iterates
We construct some much simpler sequences which, as n → ∞, are asymptotically equal in the operator norm to Vkn. This leads to a simple asymptotic formula for ||Vkn|| and to a simple ‘asymptotically extremal sequence’; that is, a sequence (un) in Lp (0, 1) with ||un||p=1 and
as n → ∞. As an application, we derive a limit theorem for large deviations, which appears to be beyond the established theory. 相似文献
15.
We prove that the so-called Smoluchowski-Kramers approximation holds for a class of partial differential equations perturbed
by a non-Gaussian noisy term. Namely, we show that the solution of the one-dimensional semi-linear stochastic damped wave
equations
, u(0) = u0, ut (0) = v0, endowed with Dirichlet boundary conditions, converges as the parameter μ goes to zero to the solution of the semi-linear
stochastic heat equation
, u(0) = u0, endowed with Dirichlet boundary conditions.
Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday 相似文献
16.
A set of positive integers is a perfect difference set if every nonzero integer has a unique representation as the difference of two elements of . We construct dense perfect difference sets from dense Sidon sets. As a consequence of this new approach we prove that there exists a perfect difference set such that
.
Also we prove that there exists a perfect difference set
such that
A(x)/≥ 1/.
The work of J. C. was supported by Grant MTM 2005-04730 of MYCIT (Spain).
The work of M. B. N. was supported in part by grants from the NSA Mathematical Sciences Program and the PSC-CUNY Research
Award Program. 相似文献
17.
Carlo F. Barenghi 《Milan Journal of Mathematics》2007,75(1):177-196
The study of vortex lines in a inviscid, incompressible Euler fluid dates back to the times of Lord Kelvin. Vortex lines are
highly idealised mathematical objects which at first sight do not seem relevant to vortices and turbulence in real fluids.
In this article I show that superfluid vortices are good physical realizations of these classical mathematical objects, and
provide us with a convenient context to investigate topological aspects of turbulence.
Received: March 2007 相似文献
18.
It is well known that there are classes of test functions such that a Hankel operator is bounded if and only if it is bounded
on those functions. Criteria are derived which determine whether a Hankel operator is compact or belongs to a particular Schatten
class, in terms of its action on those test functions. 相似文献
19.
Fritz Gesztesy Mark Malamud Marius Mitrea Serguei Naboko 《Integral Equations and Operator Theory》2009,64(1):83-113
We study generalized polar decompositions of densely defined closed linear operators in Hilbert spaces and provide some applications
to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and m-sectorial operators.
Based upon work partially supported by the US National Science Foundation under Grant Nos. DMS-0400639 and FRG-0456306, and
the Austrian Science Fund (FWF) under Grant No. Y330. 相似文献
20.