共查询到20条相似文献,搜索用时 0 毫秒
1.
Witold Majdak Zoltá n Sebestyé n Jan Stochel James E. Thomson 《Proceedings of the American Mathematical Society》2006,134(6):1687-1699
Criteria for the existence of lifts of operators intertwining subnormal operators are established. The main result of the paper reduces lifting questions for general subnormal operators to questions about lifts of cyclic subnormal operators. It is shown that in general the existence of local lifts (i.e. those coming from cyclic parts) for a pair of subnormal operators does not imply the existence of a global lift. However this is the case when minimal normal extensions of subnormal operators in question are star-cyclic.
2.
John B. Conway Kyung Hee Jin Sherwin Kouchekian 《Journal of Mathematical Analysis and Applications》2003,279(2):418-429
This paper explores properties of the Bergman operator on unbounded open subsets of the plane. In addition to the characterization of the bounded commutant of such operators it proves the Berger-Shaw theorem and gives some general criteria under which the operator and its self-commutator are densely defined. 相似文献
3.
Jan Stochel 《Proceedings of the American Mathematical Society》2001,129(8):2261-2271
The intertwining relations between cosubnormal and closed hyponormal (resp. cohyponormal and closed subnormal) operators are studied. In particular, an asymmetric Putnam-Fuglede theorem for unbounded operators is proved.
4.
A minimal normal extension of unbounded subnormal operators is established and characterized and spectral inclusion theorem
is proved. An inverse Cayley transform is constructed to obtain a closed unbounded subnormal operator from a bounded one.
Two classes of unbounded subnormals viz analytic Toeplitz operators and Bergman operators are exhibited. 相似文献
5.
B.P. Duggal 《Journal of Mathematical Analysis and Applications》2007,335(2):990-995
Necessary and sufficient conditions for hypercyclic/supercyclic Banach space operators T to satisfy are proved. 相似文献
6.
A generalized version of the Glauber-Klauder basic formula of quantum optics is shown to be valid for any cyclic subnormal operator S whose adjoint has a rich point spectrum σp(S∗) (in the sense that a semispectral measure of S vanishes on C?σp∗(S∗)). It is exhibited that such operators always have analytic models. The point spectrum of the adjoint of a subnormal operator which satisfies a generalized version of the Glauber-Klauder formula is proved to be rich (in the above sense). 相似文献
7.
8.
《Expositiones Mathematicae》2021,39(4):590-603
We generalize Moore’s nonstandard proof of the Spectral theorem for bounded self-adjoint operators to the case of unbounded operators. The key step is to use a definition of the nonstandard hull of an internally bounded self-adjoint operator due to Raab. 相似文献
9.
Xiaohong Cao 《Journal of Mathematical Analysis and Applications》2006,323(1):267-274
Using a variant of the essential approximate point spectrum, we give the necessary and sufficient conditions for T for which the a-Browder's theorem or the a-Weyl's theorem holds. Also, the relation between hypercyclic operators (or supercyclic operators) and the operators which satisfy Weyl type theorem is discussed. 相似文献
10.
Nathan S. Feldman Paul McGuire 《Proceedings of the American Mathematical Society》2005,133(5):1357-1364
We show how to compute the Fredholm index of a Toeplitz operator with a continuous symbol constructed from any subnormal operator with compact self-commutator. We also show that the essential spectral pictures of such Toeplitz operators can be prescribed arbitrarily.
11.
We prove an abstract mean ergodic theorem and use it to show that if is a sequence of commuting -dissipative (or normal) operators on a Banach space , then the intersection of their null spaces is orthogonal to the linear span of their ranges. It is also proved that the inequality holds for any -dissipative operator . These results either generalize or improve the corresponding results of Shaw, Mattila, and Crabb and Sinclair, respectively.
12.
In this paper, we extend the Perron-Frobenius theorem for positive polynomial operators in Banach lattices. The result obtained
is applied to derive necessary and sufficient conditions for the stability of positive polynomial operators. Then we study
stability radii: complex, real and positive radii of positive polynomial operators and show that in this case the three radii
coincide and can be computed by a simple formula. Finally, a simple example is given to illustrate the obtained results. 相似文献
13.
B.P. Duggal 《Journal of Mathematical Analysis and Applications》2008,340(1):366-373
A Banach space operator T∈B(X) is hereditarily polaroid, T∈HP, if every part of T is polaroid. HP operators have SVEP. It is proved that if T∈B(X) has SVEP and R∈B(X) is a Riesz operator which commutes with T, then T+R satisfies generalized a-Browder's theorem. If, in particular, R is a quasi-nilpotent operator Q, then both T+Q and T∗+Q∗ satisfy generalized a-Browder's theorem; furthermore, if Q is injective, then also T+Q satisfies Weyl's theorem. If A∈B(X) is an algebraic operator which commutes with the polynomially HP operator T, then T+N is polaroid and has SVEP, f(T+N) satisfies generalized Weyl's theorem for every function f which is analytic on a neighbourhood of σ(T+N), and f∗(T+N) satisfies generalized a-Weyl's theorem for every function f which is analytic on, and constant on no component of, a neighbourhood of σ(T+N). 相似文献
14.
We study the Grushin operators acting on \(\mathbb{R}_x^{{d_1}} \times \mathbb{R}_t^{{d_2}}\) and defined by the formula \(L = - \sum\nolimits_{j = 1}^{{d_1}} {\partial _{{x_j}}^2} - {\sum\nolimits_{j = 1}^{{d_1}} {\left| {{x_j}} \right|} ^2}\sum\nolimits_{k = 1}^{{d_2}} {\partial _{{t_k}}^2} \). We establish a restriction theorem associated with the considered operators. Our result is an analogue of the restriction theorem on the Heisenberg group obtained by D. M¨uller [Ann. of Math., 1990, 131: 567–587]. 相似文献
15.
Mircea Dan Voisei 《Journal of Mathematical Analysis and Applications》2010,371(2):661-664
In his 2008 book “From Hahn-Banach to Monotonicity”, S. Simons mentions that the proof of Lemma 41.3, which was presented in the previous edition of his book “Minimax and Monotonicity” in 1998, is incorrect, and one does not know if this lemma and its consequences are true. The aim of this short note is not only to give a proof to the mentioned lemma but also to improve upon it by relaxing one of its assumptions. 相似文献
16.
A note on Weyl's theorem for operator matrices 总被引:5,自引:0,他引:5
Slavisa V. Djordjevic Young Min Han 《Proceedings of the American Mathematical Society》2003,131(8):2543-2547
When and are given we denote by an operator acting on the Banach space of the form
In this note we examine the relation of Weyl's theorem for and through local spectral theory.
In this note we examine the relation of Weyl's theorem for and through local spectral theory.
17.
In this paper, with the help of spectral integral, we show a quantitative version of the Bishop-Phelps theorem for operators in complex Hilbert spaces. Precisely, let H be a complex Hilbert space and 0 ε 1/2. Then for every bounded linear operator T : H → H and x0 ∈ H with ||T|| = 1 = ||x0|| such that ||Tx0|| 1 ε, there exist xε∈ H and a bounded linear operator S : H → H with||S|| = 1 = ||xε|| such that ||Sxε|| = 1, ||xε-x0|| ≤ (2ε)1/2 + 4(2ε)1/2, ||S-T|| ≤(2ε)1/2. 相似文献
18.
A celebrated theorem of Coburn asserts that, on the setting of the Hardy space, if a Toeplitz operator is nonzero, then either it is one-to-one or its adjoint operator is one-to-one. In this paper, we show that an analogous result holds for Toeplitz operators acting on the Dirichlet space. 相似文献
19.
H. Zguitti 《Journal of Mathematical Analysis and Applications》2006,316(1):373-381
We prove that if either T or T∗ has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every f∈H(σ(T)). An application is given for algebraically paranormal operators. 相似文献
20.
We establish a comparison principle for quasilinear elliptic operators in unbounded cylindrical domains by combining the traditional test function method with nonlinear capacity techniques. Some applications to monotonicity and symmetry of solutions to nonlinear elliptic problems are given. 相似文献