共查询到20条相似文献,搜索用时 15 毫秒
1.
Thomas L. Kriete Barbara D. MacCluer Jennifer L. Moorhouse 《Israel Journal of Mathematics》2010,179(1):449-477
Let ϕ be a linear-fractional self-map of the open unit disk D, not an automorphism, such that ϕ(ζ) = η for two distinct points ζ,η in the unit circle ∂D. We consider the problem of determining which composition operators, acting on the Hardy space H
2, lie in C*(C
ϕ
,K), the unital C*-algebra generated by the composition operator C
ϕ
and the ideal K of compact operators. This necessitates a companion study of the unital C*-algebra generated by the composition operators induced by all parabolic non-automorphisms with common fixed point on the
unit circle. 相似文献
2.
Let ϕ be an analytic self-map and u be a fixed analytic function on the open unit disk D in the complex plane ℂ. The weighted composition operator is defined by
Weighted composition operators from Bergman-type spaces into Bloch spaces and little Bloch spaces are characterized by function
theoretic properties of their inducing maps. 相似文献
3.
B. I. Peleshenko 《Ukrainian Mathematical Journal》2005,57(11):1741-1762
We prove theorems on interpolation of quasilinear operators of weak type (ϕ0, ψ0, ϕ0, ψ1) in Lorentz spaces. The operators under study are analogs of the Calderón operator and the Benett operator for concave and
convex functions ϕ0(t), ψ0(t), ϕ1(t), and ψ1(t).
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 11, pp. 1490–1507, November, 2005. 相似文献
4.
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
5.
We determine the spectra of weighted composition operators acting on the weighted Banach spaces of analytic functionsH
ν
p
∞ when the symbolφ has a fixed point in the open unit disk. Further, we apply this result to give the spectra of composition operators on Bloch
type spaces. In particular, we answer in the affirmative a conjecture by MacCluer and Saxe.
The research of the second author was partially supported by the Academy of Finland Project No. 51906; the research of this
paper was carried out while this author was visiting Kent State University, whose hospitality is acknowledged with thanks. 相似文献
6.
Let λ and μ be solid sequence spaces. For a sequence of modulus functions Φ = (ϕ k) let λ(Φ) = {x = (x
k
): (ϕk(|x
k
|)) ∈ λ}. Given another sequence of modulus functions Ψ = (ψk), we characterize the continuity of the superposition operators P
f
from λ(Φ) into μ (Ψ) for some Banach sequence spaces λ and μ under the assumptions that the moduli ϕk (k ∈ ℕ) are unbounded and the topologies on the sequence spaces λ(Φ) and μ(Ψ) are given by certain F-norms. As applications
we consider superposition operators on some multiplier sequence spaces of Maddox type.
This research was supported by Estonian Science Foundation Grant 5376. 相似文献
7.
Whenϕ is an analytic map of the unit diskU into itself, andX is a Banach space of analytic functions onU, define the composition operatorC
ϕ
byC
ϕ
(f)=f o ϕ, forf∈X. In this paper we show how to use the Calderón theory of complex interpolation to obtain information on the spectrum ofC
ϕ
(under suitable hypotheses onϕ) acting on the Bloch spaceB and BMOA, the space of analytic functions in BMO. To do this we first obtain some results on the essential spectral radius
and spectrum ofC
ϕ
on the Bergman spacesA
pand Hardy spacesH
p,spaces which are connected toB and BMOA by the interpolation relationships [A
1,B]
t
=A
pand [H
1,BMOA]
t
=H
pfor 1=p(1−t). 相似文献
8.
We investigate the adjoints of linear fractional composition operators Cφ acting on classical Dirichlet space D(BN ) in the unit ball BN of CN , and characterize the normality and essential normality of Cφ on D(BN ) and the Dirichlet space modulo constant function D0(BN ), where φ is a linear fractional map of BN . In addition, we also show that for any non-elliptic linear fractional map φ of BN , the composition maps σ ο φ and φ ο σ are elliptic or parabolic linear fractional maps of BN . 相似文献
9.
In this paper, we study the weighted compositon operators on weighted Bergman spaces of bounded symmetric domains. The necessary
and sufficient conditions for a weighted composition operator W
φψ to be bounded and compact are studied by using the Carleson measure techniques. In the last section, we study the Schatten
p-class weighted composition operators. 相似文献
10.
Michael Koren 《Israel Journal of Mathematics》1973,15(4):396-403
It is shown that the realizability of the sequences ϕ=(a
1,…,
a
), ψ=(b
1,…,b
n
) and ϕ+ψ is a sufficient condition for the realizability of ϕ+ψ by a graph with a ϕ-factor ifb
i
≦1 fori=1,…,n. The condition is not sufficient in general. A necessary and sufficient condition for the realizability of ϕ+ψ by a graph
with a ϕ-factor is given for the case that ϕ is realizable by a star and isolated vertices. 相似文献
11.
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
12.
We characterize hyponormal “rational” Toeplitz pairs which are pairs of Toeplitz operators whose symbols are rational functions
in L∞. The main result of this article is as follows. If T = (Tϕ, Tψ) is a hyponormal rational Toeplitz pair then ϕ − βψ ∈H2 for some constant β; in other words, their co-analytic parts necessarily coincide up to a constant multiple. As a corollary we get a complete
characterization of hyponormal rational Toeplitz pairs. 相似文献
13.
Yoshinori Hamahata 《manuscripta mathematica》1993,79(1):307-327
We define the tensor product ϕ ⊗ ψ and relatedt-modules Sym2(ϕ), and ∧2(ϕ) for Drinfeld modules ϕ, ψ defined over the rational function fieldK=F
q
(T), and describe thev-adic Tate modules of theset-modules by using those of ϕ, ψ. 相似文献
14.
Stevo Stevi? 《Applied mathematics and computation》2010,216(12):3634-4972
We characterize the boundedness and compactness of weighted differentiation composition operators from the space of bounded analytic functions, the Bloch space and the little Bloch space to nth weighted-type spaces on the unit disk. 相似文献
15.
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
16.
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
17.
The Essential Norm of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions
Olli Hyv?rinen Mika Kemppainen Mikael Lindstr?m Antti Rautio Erno Saukko 《Integral Equations and Operator Theory》2012,72(2):151-157
For a wide class of radial weights we calculate the essential norm of a weighted composition operator uCj{uC_\varphi} on the weighted Banach spaces of analytic functions in terms of the analytic function
u \colon \mathbb D ? \mathbb C{u \colon \mathbb D \to \mathbb C} and the nth power of the analytic selfmap j{\varphi} of the open unit disc
\mathbb D{\mathbb D} . We also apply our result to calculate the essential norm of composition operators acting on Bloch type spaces with general
radial weights. 相似文献
18.
A. I. Petrosyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2011,46(5):264-272
The paper studies some bounded operators in the Banach spaces L
∞(B) and L
1(B) over the unit ball B of ℂ
n
, the range of which are the corresponding holomorphic subspaces A
∞(φ) and A
1(ϕ) depending on a normal pair of weight-functions {φ, ϕ}. 相似文献
19.
Andrei Heilper 《Israel Journal of Mathematics》1979,34(1-2):1-11
Let {Zn=1{(
n
∓
) bea sequence of points in the unit open disk, and letNϕ(U) denote the class of functionsf analytic in the unit disk U such that |f|∈L (
ϕ
1
)(U). For ϕ ≡ 1, the necessary and sufficient conditions for the existence off εN(U) and vanishing atz
n is Σ(
n=1
∓
) (1–|Zn|)2 ∞. Also we estimate a large family of canonical products. These results are extended to ϕ(z)=(1-|z|)ϕ.
This represents a part of a Ph.D. thesis conducted at the Technion — Israel Institute of Technology, Department of Mathematics,
by Dr. C. A. Horowitz. His help during the preparation of this paper is gratefully acknowledged. 相似文献
20.
Let ψ be a holomorphic function on the open unit disk D and φ a holomorphic self-map of D. Let Cφ,Mψ and D denote the composition, multiplication and differentiation operator, respectively. We find an asymptotic expression for the essential norm of products of these operators on weighted Bergman spaces on the unit disk. This paper is a continuation of our recent paper concerning the boundedness of these operators on weighted Bergman spaces. 相似文献