共查询到20条相似文献,搜索用时 335 毫秒
1.
Carme Cascante Joan Fàbrega Daniel Pascuas 《Integral Equations and Operator Theory》2011,69(3):373-391
For weighted Toeplitz operators TNj{{\mathcal T}^N_\varphi} defined on spaces of holomorphic functions in the unit ball, we derive regularity properties of the solutions f to the equation TNj(f)=h{{\mathcal T}^N_\varphi(f)=h} in terms of the regularity of the symbol φ and the data h. As an application, we deduce that if
f\not o 0{f\not\equiv0} is a function in the Hardy space H
1 such that its argument [`(f)]/f{\bar f/f} is in a Lipschitz space on the unit sphere
\mathbb S{{\mathbb S}}, then f is also in the same Lipschitz space, extending a result of Dyakonov to several complex variables. 相似文献
2.
H. Turgay Kaptano?lu 《Indagationes Mathematicae》2006,17(3):407-423
We investigate a Bohr phenomenon on the spaces of solutions of weighted Laplace-Beltrami operators associated with the hyperbolic metric of the unit ball in ?N. These solutions do not satisfy the usual maximum principle, and the spaces have natural bases none of whose members is a constant function. We show that these bases exhibit a Bohr phenomenon, define a Bohr radius for them that extends the classical Bohr radius, and compute it exactly. We also compute the classical Bohr radius of the invariant harmonic functions on the real hyperbolic space. 相似文献
3.
Dr. Kazimierz Wŀodarczyk 《Monatshefte für Mathematik》1983,96(4):325-330
HereJ *-algebras are considered, i.e. linear spaces of operators mapping one complex Hilbert space into another, which have a kind of Jordan triple product structure. Balls are determined which contain the sets of values of functionalsf(S) (S any fixed operator) defined on the classes of (Fréchet-)holomorphic mapsf of the unit ball into the generalized upper half-plane and of the unit ball into the unit ball, respectively (see Theorems 1 and 2). Similar results were obtained for holomorphic maps of operators in the sense of functional calculus (see Theorems 3–5). 相似文献
4.
Let A be a uniform algebra on a compact space X. An inner function is a function in A unimodular on X. For three algebras of type H∞ we prove A is generated by its inner functions. Whenever A is generated by its inner functions we prove the unit ball of A is the closed convex ball of the inner functions. 相似文献
5.
P.N. Dowling 《Journal of Functional Analysis》2008,255(3):768-775
A Banach space has the weak fixed point property if its dual space has a weak∗ sequentially compact unit ball and the dual space satisfies the weak∗ uniform Kadec-Klee property; and it has the fixed point property if there exists ε>0 such that, for every infinite subset A of the unit sphere of the dual space, A∪(−A) fails to be (2−ε)-separated. In particular, E-convex Banach spaces, a class of spaces that includes the uniformly nonsquare spaces, have the fixed point property. 相似文献
6.
Anders Olofsson 《Journal of Functional Analysis》2006,236(2):517-545
We consider a class of bounded linear operators on Hilbert space called n-hypercontractions which relates naturally to adjoint shift operators on certain vector-valued standard weighted Bergman spaces on the unit disc. In the context of n-hypercontractions in the class C0⋅ we introduce a counterpart to the so-called characteristic operator function for a contraction operator. This generalized characteristic operator function Wn,T is an operator-valued analytic function in the unit disc whose values are operators between two Hilbert spaces of defect type. Using an operator-valued function of the form Wn,T, we parametrize the wandering subspace for a general shift invariant subspace of the corresponding vector-valued standard weighted Bergman space. The operator-valued analytic function Wn,T is shown to act as a contractive multiplier from the Hardy space into the associated standard weighted Bergman space. 相似文献
7.
We study three different problems in the area of Toeplitz operators on the Segal-Bargmann space in Cn. Extending results obtained previously by the first author and Y.L. Lee, and by the second author, we first determine the commutant of a given Toeplitz operator with a radial symbol belonging to the class Sym>0(Cn) of symbols having certain growth at infinity. We then provide explicit examples of zero-products of non-trivial Toeplitz operators. These examples show the essential difference between Toeplitz operators on the Segal-Bargmann space and on the Bergman space over the unit ball. Finally, we discuss the “finite rank problem”. We show that there are no non-trivial rank one Toeplitz operators Tf for f∈Sym>0(Cn). In all these problems, the growth at infinity of the symbols plays a crucial role. 相似文献
8.
Romain Tessera 《Journal of Functional Analysis》2010,259(11):2793-2813
It is known that the algebra of Schur operators on ?2 (namely operators bounded on both ?1 and ?∞) is not inverse-closed. When ?2=?2(X) where X is a metric space, one can consider elements of the Schur algebra with certain decay at infinity. For instance if X has the doubling property, then Q. Sun has proved that the weighted Schur algebra Aω(X) for a strictly polynomial weight ω is inverse-closed. In this paper, we prove a sharp result on left-invertibility of the these operators. Namely, if an operator A∈Aω(X) satisfies ‖Afp‖?‖fp‖, for some 1?p?∞, then it admits a left-inverse in Aω(X). The main difficulty here is to obtain the above inequality in ?2. The author was both motivated and inspired by a previous work of Aldroubi, Baskarov and Krishtal (2008) [1], where similar results were obtained through different methods for X=Zd, under additional conditions on the decay. 相似文献
9.
Let T∈Bn(H) be an essentially normal spherical isometry with empty point spectrum on a separable complex Hilbert space H, and let AT⊂B(H) be the unital dual operator algebra generated by T. In this note we show that every operator S∈B(H) in the essential commutant of AT has the form S=X+K with a T-Toeplitz operator X and a compact operator K. Our proof actually covers a larger class of subnormal operator tuples, called A-isometries, which includes for example the tuple T=(Mz1,…,Mzn)∈B(H2n(σ)) consisting of the multiplication operators with the coordinate functions on the Hardy space H2(σ) associated with the normalized surface measure σ on the boundary ∂D of a strictly pseudoconvex domain D⊂Cn. As an application we determine the essential commutant of the set of all analytic Toeplitz operators on H2(σ) and thus extend results proved by Davidson (1977) [6] for the unit disc and Ding and Sun (1997) [11] for the unit ball. 相似文献
10.
If
\mathfrakA{\mathfrak{A}} is a unital weak-* closed algebra of multiplication operators on a reproducing kernel Hilbert space which has the property
\mathbbA1(1){\mathbb{A}_1(1)}, then the cyclic invariant subspaces index a Nevanlinna–Pick family of kernels. This yields an NP interpolation theorem for
a wide class of algebras. In particular, it applies to many function spaces over the unit disk including Bergman space. We
also show that the multiplier algebra of a complete NP space has
\mathbbA1(1){\mathbb{A}_1(1)}, and thus this result applies to all of its subalgebras. A matrix version of this result is also established. It applies,
in particular, to all unital weak-* closed subalgebras of H
∞ acting on Hardy space or on Bergman space. 相似文献
11.
Tavan T. Trent 《Integral Equations and Operator Theory》2013,75(2):151-164
Let ${\mathcal{A}}$ denote the multiplier algebra of an E-valued reproducing kernel Hilbert space, ${H_E^2(k)}$ . Then when H 2(k) is nice, we give necessary and sufficient conditions that T > 0 factors as A*A, where A and ${A^{-1} \in \mathcal{A}}$ . Such nice spaces include the Bergman and Hardy spaces on the unit polydisk and unit ball in ${\mathbb{C}^d}$ . 相似文献
12.
We investigate the relationships between smooth and strongly smooth points of the unit ball of an order continuous symmetric
function space E, and of the unit ball of the space of τ-measurable operators E(M,t){E(\mathcal{M},\tau)} associated to a semifinite von Neumann algebra (M, t){(\mathcal{M}, \tau)}. We prove that x is a smooth point of the unit ball in E(M, t){E(\mathcal{M}, \tau)} if and only if the decreasing rearrangement μ(x) of the operator x is a smooth point of the unit ball in E, and either μ(∞; f) = 0, for the function f ? SE×{f\in S_{E^{\times}}} supporting μ(x), or s(x
*) = 1. Under the assumption that the trace τ on M{\mathcal{M}} is σ-finite, we show that x is strongly smooth point of the unit ball in E(M, t){E(\mathcal{M}, \tau)} if and only if its decreasing rearrangement μ(x) is a strongly smooth point of the unit ball in E. Consequently, for a symmetric function space E, we obtain corresponding relations between smoothness or strong smoothness of the function f and its decreasing rearrangement μ(f). Finally, under suitable assumptions, we state results relating the global properties such as smoothness and Fréchet smoothness
of the spaces E and E(M,t){E(\mathcal{M},\tau)}. 相似文献
13.
The reflexivity and transitivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane are investigated. The dichotomic behavior (transitive or reflexive) of these subspaces is shown. It refers to the similar dichotomic behavior for subspaces of Toeplitz operators on the Hardy space on the unit disc. The isomorphism between the Hardy spaces on the unit disc and the upper half-plane is used. To keep weak* homeomorphism between L ∞ spaces on the unit circle and the real line we redefine the classical isomorphism between L 1 spaces. 相似文献
14.
Eric Amar 《Indagationes Mathematicae》2007,18(2):177-187
Let A be a uniform algebra on the compact space X and σ a probability measure on X. We define the Hardy spaces HP(σ) and the HP(σ) interpolating sequences S in the p-spectrum Mp of σ. Under some structural hypotheses on (A, σ), we prove that if a sequence S ⊂ Mp is HP(σ) interpolating, then it is Hs(σ) interpolating for s < p. In the special case of the unit ball B of ?n this answers a natural question asked in [8]. 相似文献
15.
Multiplication operators on sobolev disk algebra 总被引:2,自引:0,他引:2
WANG Zongyao & LIU Yiqiang Department of Mathematics East China University of Science Technology Shanghai China 《中国科学A辑(英文版)》2005,48(10):1395-1410
In this paper,we study the algebra consisting of analytic functions in the Sobolev space W~(2,2) (D) (D is the unit disk),called the Sobolev disk algebra,explore the properties of the multiplication operators M_f on it and give the characterization of the corn- mutant algebra A′(M_f) of M_f.We show that A′(M_f) is commutative if and only if M_f~* is a Cowen-Douglas operator of index 1. 相似文献
16.
17.
We prove that Fredholm composition operators acting on the uniform algebra H∞(BE) of bounded analytic functions on the open unit ball of a complex Banach space E with the approximation property are invertible and arise from analytic automorphisms of the ball. 相似文献
18.
Sebastian Król 《Journal of Evolution Equations》2013,13(2):281-309
The paper provides new characterisations of generators of cosine functions and C 0-groups on UMD spaces and their applications to some classical problems in cosine function theory. In particular, we show that on UMD spaces, generators of cosine functions and C 0-groups can be characterised by means of a complex inversion formula. This allows us to provide a strikingly elementary proof of Fattorini’s result on square root reduction for cosine function generators on UMD spaces. Moreover, we give a cosine function analogue of McIntosh’s characterisation of the boundedness of the H ∞ functional calculus for sectorial operators in terms of square function estimates. Another result says that the class of cosine function generators on a Hilbert space is exactly the class of operators which possess a dilation to a multiplication operator on a vector-valued L 2 space. Finally, we prove a cosine function analogue of the Gomilko-Feng-Shi characterisation of C 0-semigroup generators and apply it to answer in the affirmative a question by Fattorini on the growth bounds of perturbed cosine functions on Hilbert spaces. 相似文献
19.
Oh Sang Kwon 《Applied mathematics and computation》2011,218(3):912-918
Let A be the class of analytic functions in the open unit disk U. A function f in A satisfying the normalization is said to be in the class SPn if Dnf is a parabolic starlike function, where Dn is a notation of the Salagean operator. In this paper, several basic properties and characteristics of the class SPn are investigated. These include subordination, convolution properties, class-preserving integral operators, and Fekete-Szegö problems. 相似文献
20.
In this paper we introduce a generalized Sobolev space by defining a semi-inner product formulated in terms of a vector distributional
operator P consisting of finitely or countably many distributional operators P
n
, which are defined on the dual space of the Schwartz space. The types of operators we consider include not only differential
operators, but also more general distributional operators such as pseudo-differential operators. We deduce that a certain
appropriate full-space Green function G with respect to L := P
*T
P now becomes a conditionally positive function. In order to support this claim we ensure that the distributional adjoint operator
P
* of P is well-defined in the distributional sense. Under sufficient conditions, the native space (reproducing-kernel Hilbert space)
associated with the Green function G can be embedded into or even be equivalent to a generalized Sobolev space. As an application, we take linear combinations
of translates of the Green function with possibly added polynomial terms and construct a multivariate minimum-norm interpolant
s
f,X
to data values sampled from an unknown generalized Sobolev function f at data sites located in some set
X ì \mathbbRd{X \subset \mathbb{R}^d}. We provide several examples, such as Matérn kernels or Gaussian kernels, that illustrate how many reproducing-kernel Hilbert
spaces of well-known reproducing kernels are equivalent to a generalized Sobolev space. These examples further illustrate
how we can rescale the Sobolev spaces by the vector distributional operator P. Introducing the notion of scale as part of the definition of a generalized Sobolev space may help us to choose the “best”
kernel function for kernel-based approximation methods. 相似文献