共查询到20条相似文献,搜索用时 46 毫秒
1.
Insook Kim Yoenha Kim Eungil Ko Ji Eun Lee 《Journal of Mathematical Analysis and Applications》2008,340(2):1235-1240
In this paper we show that the nilpotent perturbation of operators in the Helton class of p-hyponormal operators has scalar extensions. As a corollary we get that the nilpotent perturbation of each operator in the Helton class of p-hyponormal operators has a nontrivial invariant subspace if its spectrum has nonempty interior in the plane. 相似文献
2.
The class of -hyponormal operators is introduced. This class contains allp-hyponormal operators. Certain properties of this class of operators are obtained. Among other things, it is shown that ifT is -hyponormal, then its spectral radius and norm are identical, and the nonzero points of its joint point spectrum and point spectrum are identical. Conditions under which a -hyponormal operator becomes normal, self-adjoint and unitary are given. 相似文献
3.
We prove that for every -hyponormal operator there corresponds a hyponormal operator such that and have ``equal spectral structure". We also prove that every -hyponormal operator is subdecomposable. Then some relevant quasisimilarity results are obtained, including that two quasisimilar -hyponormal operators have equal essential spectra.
4.
In this note we examine the relationships between p-hyponormal
operators and the operator inequality
. This leads to a method for
generating examples of p-hyponormal operators which are not q-hyponormal
for any
. Our methods are also shown to have implications for the class
of Furuta type inequalities. 相似文献
5.
In this paper, we study the k-quasi-M-hyponormal operator and mainly prove that if T is a k-quasi-M-hyponormal operator, then \(\sigma _{ja}(T)\backslash \{0\}=\sigma _{a}(T)\backslash \{0\}\), and the spectrum is continuous on the class of all k-quasi-M-hyponormal operators; let \(d_{AB}\in B(B(H))\) denote either the generalized derivation \(\delta _{AB}= L_{A}-R_{B}\) or the elementary operator \(\Delta _{AB} =L_{A}R_{B}- I\), we show that if A and \(B^{*}\) are k-quasi-M-hyponormal operators, then \(d_{AB}\) is polaroid and generalized Weyl’s theorem holds for \(f(d_{AB})\), where f is an analytic function on \(\sigma (d_{AB})\) and f is not constant on each connected component of the open set U containing \(\sigma (d_{AB})\). In additon, we discuss the hyperinvariant subspace problem for k-quasi-M-hyponormal operators. 相似文献
6.
L. Maniccia E. Schrohe J. Seiler 《Proceedings of the American Mathematical Society》2008,136(2):747-752
Let be a closed manifold. We show that the Kontsevich-Vishik trace, which is defined on the set of all classical pseudodifferential operators on , whose (complex) order is not an integer greater than or equal to , is the unique functional which (i) is linear on its domain, (ii) has the trace property and (iii) coincides with the -operator trace on trace class operators.
Also the extension to even-even pseudodifferential operators of arbitrary integer order on odd-dimensional manifolds and to even-odd pseudodifferential operators of arbitrary integer order on even-dimensional manifolds is unique.
7.
Gerardo A. Chacó n Gerardo R. Chacó n José Gimé nez 《Proceedings of the American Mathematical Society》2007,135(7):2205-2218
In this paper we study composition operators on spaces of entire functions. We determine which entire functions induce bounded composition operators on the Paley-Wiener space, , and on the spaces. In addition, we characterize compact composition operators on these spaces. We also study the cyclic properties of composition operators acting on .
8.
Yang Changsen Li Haiying 《高校应用数学学报(英文版)》2006,21(1):64-68
The approximate point spectrum properties of p-ω-hyponormal operators are given and proved. In faet, it is a generalization of approximate point speetrum properties of ω- hyponormal operators. The relation of spectra and numerical range of p-ω-hyponormal operators is obtained, On the other hand, for p-ω-hyponormal operators T,it is showed that if Y is normal,then T is also normal. 相似文献
9.
Eungil Ko 《Proceedings of the American Mathematical Society》2000,128(3):775-780
In this paper we show that -hyponormal operators with are subscalar. As a corollary, we get that such operators with rich spectra have non-trivial invariant subspaces.
10.
Wojciech Bartoszek Beata Kuna 《Proceedings of the American Mathematical Society》2005,133(7):2119-2129
We show that the set of those Markov operators on the Schatten class such that , where is one-dimensional projection, is norm open and dense. If we require that the limit projections must be on strictly positive states, then such operators form a norm dense . Surprisingly, for the strong operator topology operators the situation is quite the opposite.
11.
In this paper, we show that algebraic extensions of semi-hyponormal operators (defined below) are subscalar. As corollaries we get the following:
From these results and [Es] it is known that such operators with rich spectra have nontrivial invariant subspaces.The second author was supported by the grant for the promotion of scientic research in women's universities. 相似文献
(1) | Everyk-quasihyponormal operator is subscalar. |
(2) | Every algebraic extension of Aluthge transforms ofp-hyponormal operators is subscalar. |
12.
Edward Kissin 《Proceedings of the American Mathematical Society》2007,135(8):2483-2495
In this paper we obtain analogues of Clarkson-McCarthy inequalities for -tuples of operators from Schatten ideals . Using them, we extend the results of Bhatia and Kittaneh on inequalities for partitioned operators and for Cartesian decomposition of operators from .
13.
Oleg N. Ageev 《Proceedings of the American Mathematical Society》2003,131(7):2053-2062
Let be an off-diagonal joining of a transformation . We construct a non-typical transformation having asymmetry between limit sets of for positive and negative powers of . It follows from a correspondence between subpolymorphisms and positive operators, and from the structure of limit polynomial operators. We apply this technique to find all polynomial operators of degree in the weak closure (in the space of positive operators on ) of powers of Chacon's automorphism and its generalizations.
14.
Il Bong Jung Mi Ryeong Lee Sang Soo Park 《Proceedings of the American Mathematical Society》2007,135(12):3955-3965
Several classes have been considered to study the weak subnormalities of Hilbert space operators. One of them is -hypnormality, which comes from the Bram-Halmos criterion for subnormal operators. In this note we consider -hyponormality, which is the parallel version corresponding to the Embry characterization for subnormal operators. We characterize -hyponormality of composition operators via -th Radon-Nikodym derivatives and present some examples to distinguish the classes.
15.
16.
Thomas R. Shemanske 《Transactions of the American Mathematical Society》2007,359(7):3409-3423
In this paper, we investigate both arithmetic and combinatorial aspects of buildings and associated Hecke operators for with a local field. We characterize the action of the affine Weyl group in terms of a symplectic basis for an apartment, characterize the special vertices as those which are self-dual with respect to the induced inner product, and establish a one-to-one correspondence between the special vertices in an apartment and the elements of the quotient .
We then give a natural representation of the local Hecke algebra over acting on the special vertices of the Bruhat-Tits building for . Finally, we give an application of the Hecke operators defined on the building by characterizing minimal walks on the building for .
17.
In this paper we prove the smoothness of solutions of a class of elliptic-parabolic nonlinear Levi type equations, represented as a sum of squares plus a vector field. By means of a freezing method the study of the operator is reduced to the analysis of a family of left invariant operators on a free nilpotent Lie group. The fundamental solution of the operator is used as a parametrix of the fundamental solution of the Levi operator, and provides an explicit representation formula for the solution of the given equation. Differentiating this formula and applying a bootstrap method, we prove that the solution is .
18.
Eva A. Gallardo-Gutié rrez Marí a J. Gonzá lez Artur Nicolau 《Transactions of the American Mathematical Society》2008,360(1):395-410
For any simply connected domain , we prove that a Littlewood type inequality is necessary for boundedness of composition operators on , , whenever the symbols are finitely-valent. Moreover, the corresponding ``little-oh' condition is also necessary for the compactness. Nevertheless, it is shown that such an inequality is not sufficient for characterizing bounded composition operators even induced by univalent symbols. Furthermore, such inequality is no longer necessary if we drop the extra assumption on the symbol of being finitely-valent. In particular, this solves a question posed by Shapiro and Smith (2003). Finally, we show a striking link between the geometry of the underlying domain and the symbol inducing the composition operator in , and in this sense, we relate both facts characterizing bounded and compact composition operators whenever is a Lavrentiev domain.
19.
Kasso A. Okoudjou Robert S. Strichartz 《Proceedings of the American Mathematical Society》2007,135(8):2453-2459
In this note we investigate the asymptotic behavior of spectra of Schrödinger operators with continuous potential on the Sierpinski gasket . In particular, using the existence of localized eigenfunctions for the Laplacian on we show that the eigenvalues of the Schrödinger operator break into clusters around certain eigenvalues of the Laplacian. Moreover, we prove that the characteristic measure of these clusters converges to a measure. Results similar to ours were first observed by A. Weinstein and V. Guillemin for Schrödinger operators on compact Riemannian manifolds.
20.
Neil Lyall 《Transactions of the American Mathematical Society》2007,359(9):4467-4488
We consider the mapping properties of a model class of strongly singular integral operators on the Heisenberg group ; these are convolution operators on whose kernels are too singular at the origin to be of Calderón-Zygmund type. This strong singularity is compensated for by introducing a suitably large oscillation.
Our results are obtained by utilizing the group Fourier transform and uniform asymptotic forms for Laguerre functions due to Erdélyi.