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1.
We investigate properties of composition operators C? on the Newton space (the Hilbert space of analytic functions which have the Newton polynomials as an orthonormal basis). We derive a formula for the entries of the matrix of C? with respect to the basis of Newton polynomials in terms of the value of the symbol ? at the non-negative integers. We also establish conditions on the symbol ? for boundedness, compactness, and self-adjointness of the induced composition operator C?. A key technique in obtaining these results is use of an isomorphism between the Newton space and the Hardy space via the Binomial Theorem. 相似文献
2.
Abdolaziz Abdollahi 《Rendiconti del Circolo Matematico di Palermo》2009,58(2):257-264
Let T be an operator on a Hilbert space . The problem of computing of the norm of T, norm of selfcommutators of T, and the numerical radius of T are discussed in many papers and a number of textbooks. In this paper we determine the relationships between these values
for self inverse operators and explain how we can determine any three of these (‖T‖, ‖[T*,T]‖, ‖{T*,T}‖, and the numerical radius of T) by knowing any one of them. Also, we find the spectrum of T*T,[T*,T] and {T*,T} in the case that T is self inverse and the spectrum of T*T is an interval. Finally, by giving some examples on automorphic composition operators, we show that these results make it
possible to replace lengthy computation with quick ones.
Research partially supported by the Shiraz university Research Council Grant No. 86-GR-SC-32. 相似文献
3.
Zinoviy Grinshpun 《Proceedings of the American Mathematical Society》2003,131(5):1591-1600
We prove the following theorem. Any isometric operator , that acts from the Hilbert space with nonnegative weight to the Hilbert space with nonnegative weight , allows for the integral representation
where the kernels and satisfy certain conditions that are necessary and sufficient for these kernels to generate the corresponding isometric operators.
where the kernels and satisfy certain conditions that are necessary and sufficient for these kernels to generate the corresponding isometric operators.
4.
P. Chansangiam 《Journal of Mathematical Analysis and Applications》2009,356(2):525-276
Let B(H) be the space of all bounded linear operators on a complex separable Hilbert space H. Bohr inequality for Hilbert space operators asserts that for A,B∈B(H) and p,q>1 real numbers such that 1/p+1/q=1,
2|A+B|?p2|A|+q2|B| 相似文献
5.
It is shown that an operator on the Hardy space (or ) commutes with all analytic Toeplitz operators modulo the finite rank operators if and only if . Here is a finite rank operator, and in the case , is a sum of a rational function and a bounded analytic function, and in the case , is a bounded analytic function.
6.
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
7.
Let be an infinite dimensional separable Hilbert space over the complex field. Structure characterizations are given for some elementary operators on which preserve point spectrum.
8.
苏维钢 《纯粹数学与应用数学》2006,22(3):330-334,340
讨论两个拟相似半控制算子的本质谱之间的关系,应用算子谱的精密结构的分析方法,给出拟相似半控制算子的本质谱相等的若干充分条件,所得结果改进和发展了L.R.W illiam s在文[7-8]中的有关结果. 相似文献
9.
We prove several distance formulas from a fixed operator in to some classes of operators connected with the semi-Fredholm ones. Here is a separable Hilbert space. In particular, Fredholm and upper and lower semi-Fredholm operators have the same boundary in .
10.
《Indagationes Mathematicae》2022,33(2):494-516
Current work defines Schmidt representation of a bilinear operator , where and are separable Hilbert spaces. Introducing the concept of singular value and ordered singular value, we prove that if is compact, and its singular values are ordered, then has a Schmidt representation on real Hilbert spaces. We prove that the hypothesis of existence of ordered singular values is fundamental. 相似文献
11.
12.
Dimosthenis Drivaliaris 《Journal of Mathematical Analysis and Applications》2005,305(2):560-565
Let X be a real Banach space. We prove that the existence of an injective, positive, symmetric and not strictly singular operator from X into its dual implies that either X admits an equivalent Hilbertian norm or it contains a nontrivially complemented subspace which is isomorphic to a Hilbert space. We also treat the nonsymmetric case. 相似文献
13.
Ehliman AdigüzelovYonca Sezer 《Applied mathematics and computation》2011,218(5):2113-2121
Let L0 and L be operators which are formed by the differential expressions.
?0(y)=(-1)my(2m)(x)+Ay(x) 相似文献
14.
Consider two Toeplitz operators Tg, Tf on the Segal-Bargmann space over the complex plane. Let us assume that g is a radial function and both operators commute. Under certain growth condition at infinity of f and g we show that f must be radial, as well. We give a counterexample of this fact in case of bounded Toeplitz operators but a fast growing radial symbol g. In this case the vanishing commutator [Tg,Tf]=0 does not imply the radial dependence of f. Finally, we consider Toeplitz operators on the Segal-Bargmann space over Cn and n>1, where the commuting property of Toeplitz operators can be realized more easily. 相似文献
15.
16.
Building on techniques developed by Cowen (1988) [3] and Nazarov–Shapiro (2007) [10], it is shown that the adjoint of a composition operator, induced by a unit disk-automorphism, is not strongly asymptotically Toeplitz. This result answers Nazarov–Shapiro’s question in Nazarov and Shapiro (2007) [10]. 相似文献
17.
María J. Martín 《Journal of Functional Analysis》2006,238(1):298-312
We observe that a formula for the adjoint of a composition operator, known only for special symbols in some spaces of analytic functions, actually holds for every admissible symbol and in any Hilbert space of analytic functions with reproducing kernels. Along with some new results, all known formulas for the adjoint obtained so far follow easily as a consequence, some in an improved form. 相似文献
18.
A method of approaching to the infinite-dimensional linear operators by the finite-dimensional operators is discussed. It is shown that,for every infinite-dimensional operator A and every natural number n,there exists an n-dimensional optimal approximation to A. The norm error is found and the necessary and sufficient condition for such n-dimensional optimal approximations to be unique is obtained. 相似文献
19.
R. S. Ismagilov 《Functional Analysis and Its Applications》2006,40(3):222-224
As a generalization of the well-known Racah coefficients (defined for finite-dimensional representations of semisimple Lie groups), we introduce the notion of Racah operators for locally compact groups with “nice” dual space. In the case of the group PSL(2,?), these operators are explicitly indicated. 相似文献
20.
§1. IntroductionLetHandKberealorcomplexinfinitedimensionalHilberspace.A(boundedlinear)op-eratorA:H→Kissaidtobeinfinite-dimensional(or,finite-dimensional)iftherangeofAisinfinitedimensional(or,finitedimensional).Aissaidtoben-dimensionaliftherangeofAisn… 相似文献