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1.
In this paper we investigate some algebra properties of dual Toeplitz operators on the orthogonal complement of the Dirichlet space in the Sobolev space. We completely characterize commuting dual Toeplitz operators with harmonic symbols, and show that a dual Toeplitz operator commutes with a nonconstant analytic dual Toeplitz operator if and only if its symbol is analytic. We also obtain the sufficient and necessary conditions on the harmonic symbols for SφSφψ= Sφψ. 相似文献
2.
This paper studies the connection between an analytic function φ on the unit disk and a certain type of operators induced by φ on weighted Bergman spaces A
α of analytic functions on . The general theme is the interplay between smoothness conditions on φ and the S
p
-norms of the operators induced by φ.
相似文献
3.
Continuous functions on Baire space are considered. Iteration operators are defined on a set of continuous functions. The
idea of a module of continuity of a function is introduced. The condition for the growth of module of continuity φ whose satisfaction
guarantees that for any enumerable sequence of integration operators and any natural n there exists (n + 1) argument function with the module of continuity φ which cannot be obtained from n-argument functions with the module of continuity φ using any operator of this sequence is formulated. Examples of iteration
operators are given. 相似文献
4.
In this paper, we study composition operators on a Banach space of analytic functions, denoted byX, which includes the Bloch space. This space arises naturally as the dual space of analytic functions in the Bergman spaceL
α
1
(D) which admit an atomic decomposition. We characterize the functions which induce compact composition operators and those
which induce Fredholm operatorson this space. We also investigate when a composition operator has a closed range.
Supported by NNSFC No.19671036 相似文献
5.
Jussi Laitila 《Integral Equations and Operator Theory》2007,58(4):487-502
Analytic composition operators
are studied on X-valued versions of BMOA, the space of analytic functions on the unit disk that have bounded mean oscillation on the unit
circle, where X is a complex Banach space. It is shown that if X is reflexive and C
φ is compact on BMOA, then C
φ is weakly compact on the X-valued space BMOA
C
(X) defined in terms of Carleson measures. A related function-theoretic characterization is given of the compact composition
operators on BMOA. 相似文献
6.
E. S. Dubtsov 《Siberian Mathematical Journal》2009,50(6):998-1006
Denote by Hol(B
n
) the space of all holomorphic functions in the unit ball B
n
of ℂ
n
, n ≥ 1. Given g ∈ Hol(B
m
) and a holomorphic mapping φ: B
m
→ B
n
, put C
φ
g
f = g · (f ∘ φ) for f ∈ Hol(B
n
). We characterize those g and φ for which C
φ
g
is a bounded (or compact) operator from the growth space A
−log(B
n
) or A
−β
(B
n
), β > 0, to the weighted Bergman space A
α
p
(B
m
), 0 < p < ∞, α > −1. We obtain some generalizations of these results and study related integral operators. 相似文献
7.
Valentin Matache 《Complex Analysis and Operator Theory》2008,2(1):169-197
Operators on function spaces acting by composition to the right with a fixed selfmap φ of some set are called composition operators of symbol φ. A weighted composition operator is an operator equal to a composition operator followed by a multiplication operator. We
summarize the basic properties of bounded and compact weighted composition operators on the Hilbert Hardy space on the open
unit disk and use them to study composition operators on Hardy–Smirnov spaces.
Submitted: January 30, 2007. Revised: June 19, 2007. Accepted: July 11, 2007. 相似文献
8.
This note discusses eigenvalues of weighted composition operators uC
φ
on the Bloch space. The main result provides a class of uC
φ
for which computation of eigenvalues is possible. We also construct an example of a non-compact operator C
φ
whose eigenvalues can be determined precisely. 相似文献
9.
SHARIEF DESHMUKH 《Proceedings Mathematical Sciences》2011,121(2):171-179
In this paper, we classify real hypersurfaces in the complex projective space
C P\fracn+12C P^{\frac{n+1}{2}} whose structure vector field is a φ-analytic vector field (a notion similar to analytic vector fields on complex manifolds). We also define Jacobi-type vector
fields on a Riemannian manifold and classify real hypersurfaces whose structure vector field is a Jacobi-type vector field. 相似文献
10.
J. Feldman 《Israel Journal of Mathematics》1965,3(2):99-103
A short proof of the Levy continuity theorem in Hilbert space.
In the theory of the normal distribution on a real Hilbert spaceH, certain functionsφ have been shown by L. Gross to give rise to random variablesφ∼ in a natural way; in particular, this is the case for functions which are “uniformly τ-continuous near zero”. Among such
functions are the characteristic functionsφ of probability distributionsm onH, given byφ(y)=∫e
i(y,x)dm(x). The following analogue of the Levy continuity theorem has been proved by Gross: Letφ
j be the characteristic function of the probability measurem
j onH, Then necessary and sufficient that ∫f dm
j → ∫f dm for some probability measurem and all bounded continuousf, is that there exists a functionφ, uniformly τ-continuous near zero, withφ
j∼ →φ∼ in probability.φ turns out, of course, to be the characteristic function ofm. In the present paper we give a short proof of this theorem.
Research supported by National Science Foundation Grant GP-3977. 相似文献
11.
In this article we introduce the difference sequence space m(M, Δ, φ) using the Orlicz function. We study its different properties like solidity, completeness etc. Also we obtain some inclusion
relations involving the space m(M, Δ, φ).
相似文献
12.
Richard A. Alò Andrè de Korvin Charles Roberts 《Annali di Matematica Pura ed Applicata》1977,112(1):33-48
Summary Under study is the existence of averaging operators determined by measurable maps φ from a measure space (S, Σ, μ) into an
arbitrary Hausdorff topological space T. The map φ induces a continuous map φe from the space Cb(T) into the normed (Banach) function space Lϱ = Lϱ(S, Σ, μ) defined by φe(f)=foφ for all f ε Cb(T). An integral representation for such operators is first studied. The existence is then determined by the existence of
an averaging operator U1 for the restriction of φ to a certain measurable subset B1 of S. Utilizing a representation of Lϱ(S, Σ, μ) as a Banach function space over a compact extremally disconnected Hausdorff space Ŝ, we are able to give a definition
for the concept of plural points and irreducible map. A significant upper bound is given for the operator U1. Finally conditions are considered under which no bounded projection from Lϱ onto the range of φe may exist. From a topological point of view the development is pursued in a general setting. Averaging operators have recently
been used for the study of injective Banach spaces of the type Cb(T) and in non-linear prediction and approximation theory relative to Tshebyshev subspaces of Lϱ.
Entrata in Redazione l’ll settembre 1975. 相似文献
13.
An invertible linear map φ on a Lie algebra L is called a triple automorphism of it if φ([x, [y, z]]) = [φ(x), [φ(y), φ(z)]] for ∀ x, y, z ∈ L. Let g be a finite-dimensional simple Lie algebra of rank l defined over an algebraically closed field F of characteristic zero, p an arbitrary parabolic subalgebra of g. It is shown in this paper that an invertible linear map φ on p is a triple automorphism if and only if either φ itself is an automorphism of p or it is the composition of an automorphism of p and an extremal map of order 2. 相似文献
14.
Jin Chuan HOU Xiu Ling ZHANG 《数学学报(英文版)》2006,22(1):179-186
Let X be an infinite-dimensional complex Banach space and denote by B(X) the algebra of all bounded linear operators acting on X. It is shown that a surjective additive map Φ from B(X) onto itself preserves similarity in both directions if and only if there exist a scalar c, a bounded invertible linear or conjugate linear operator A and a similarity invariant additive functional ψ on B(X) such that either Φ(T) = cATA^-1 + ψ(T)I for all T, or Φ(T) = cAT*A^-1 + ψ(T)I for all T. In the case where X has infinite multiplicity, in particular, when X is an infinite-dimensional Hilbert space, the above similarity invariant additive functional ψ is always zero. 相似文献
15.
Let E be a complex Banach space, with the unit ball B
E
. We study the spectrum of a bounded weighted composition operator u
C
φ
on H
∞(B
E
) determined by an analytic symbol φ with a fixed point in B
E
such that φ(B
E
) is a relatively compact subset of E, where u is an analytic function on B
E
. 相似文献
16.
Maribel Loaiza Marcos López-García Salvador Pérez-Esteva 《Integral Equations and Operator Theory》2005,53(2):287-296
In this paper we decompose
into diadic annuli
and consider the class Sp,q of Toeplitz operators Tφ for which the sequence of Schatten norms
belongs to ℓq, where φn = φχ An. We study the boundedness and compactness of the operators in Sp,q and we describe the operators Tφ , φ ≥ 0 in these spaces in terms of weighted Herz norms of the averaging operator of the symbols φ. 相似文献
17.
Hasi WULAN 《数学学报(英文版)》2005,21(6):1415-1424
Suppose that φ is an analytic self-map of the unit disk Δ. We consider compactness of the composition operator Cφ from the Bloch space B into the spaces QK defined by a nonnegative, nondecreasing function K(r) for 0 ≤ r 〈 Cφ. Our compactness condition depends only on Φ which can be considered as a slight improvement of the known results. The compactness of Cφ from the Dirichlet space D into the spaces QK is also investigated, 相似文献
18.
Compact composition operators on the Bloch space in polydiscs 总被引:1,自引:0,他引:1
Let Un be the unit polydisc of ℂn and φ=(φ1, ⋯, φ
n
) a holomorphic self-map of Un. As the main result of the paper, it shows that the composition operator C is compact on the Bloch space β(Un) if and only if for every ε > 0, there exists a δ > 0, such that
whenever dist(φ(z), ∂U
n
)<δ. 相似文献
19.
Ursula Hamenstädt 《Inventiones Mathematicae》2009,176(2):223-273
Let S be an oriented surface of genus g≥0 with m≥0 punctures and 3g-3+m≥2. We classify all Radon measures on the space of measured geodesic laminations which are invariant under the action of the
mapping class group of S. 相似文献
20.
V. Yu. Protasov 《Functional Analysis and Its Applications》2011,45(1):46-55
We study continuous subadditive set-valued maps taking points of a linear space X to convex compact subsets of a linear space Y. The subadditivity means that φ(x
1 + x
2) ⊂ φ(x
1) + φ(x
2). We characterize all pairs of locally convex spaces (X, Y) for which any such map has a linear selection, i.e., there exists a linear operator A: X → Y such that Ax ∈ φ(x), x ∈ X. The existence of linear selections for a class of subadditive maps generated by differences of a continuous function is
proved. This result is applied to the Lipschitz stability problem for linear operators in Banach spaces. 相似文献