共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
Let T be a C0–contraction on a separable Hilbert space. We assume that IH − T*T is compact. For a function f holomorphic in the unit disk
\mathbbD{\mathbb{D}} and continuous on
[`(\mathbbD)]\overline{{\mathbb{D}}}, we show that f(T) is compact if and only if f vanishes on
s(T)?\mathbbT\sigma(T)\cap{\mathbb{T}}, where σ(T) is the spectrum of T and
\mathbbT{\mathbb{T}} the unit circle. If f is just a bounded holomorphic function on
\mathbbD{\mathbb{D}}, we prove that f(T) is compact if and only if limn? ¥||Tnf(T)|| = 0\lim\limits_{n\rightarrow \infty}\|T^{n}f(T)\| = 0. 相似文献
3.
A Toeplitz operator TfT_\phi with symbol f\phi in
L¥(\mathbbD)L^{\infty}({\mathbb{D}}) on the Bergman space
A2(\mathbbD)A^{2}({\mathbb{D}}), where
\mathbbD\mathbb{D} denotes the open unit disc, is radial if f(z) = f(|z|)\phi(z) = \phi(|z|) a.e. on
\mathbbD\mathbb{D}. In this paper, we consider the numerical ranges of such operators. It is shown that all finite line segments, convex hulls
of analytic images of
\mathbbD\mathbb{D} and closed convex polygonal regions in the plane are the numerical ranges of radial Toeplitz operators. On the other hand,
Toeplitz operators TfT_\phi with f\phi harmonic on
\mathbbD\mathbb{D} and continuous on
[`(\mathbbD)]{\overline{\mathbb{D}}} and radial Toeplitz operators are convexoid, but certain compact quasinilpotent Toeplitz operators are not. 相似文献
4.
V. V. Lebedev 《Functional Analysis and Its Applications》2012,46(2):121-132
We consider the space
A(\mathbbT)A(\mathbb{T}) of all continuous functions f on the circle
\mathbbT\mathbb{T} such that the sequence of Fourier coefficients
[^(f)] = { [^(f)]( k ), k ? \mathbbZ }\hat f = \left\{ {\hat f\left( k \right), k \in \mathbb{Z}} \right\} belongs to l
1(ℤ). The norm on
A(\mathbbT)A(\mathbb{T}) is defined by
|| f ||A(\mathbbT) = || [^(f)] ||l1 (\mathbbZ)\left\| f \right\|_{A(\mathbb{T})} = \left\| {\hat f} \right\|_{l^1 (\mathbb{Z})}. According to the well-known Beurling-Helson theorem, if
f:\mathbbT ? \mathbbT\phi :\mathbb{T} \to \mathbb{T} is a continuous mapping such that
|| einf ||A(\mathbbT) = O(1)\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = O(1), n ∈ ℤ then φ is linear. It was conjectured by Kahane that the same conclusion about φ is true under the assumption that
|| einf ||A(\mathbbT) = o( log| n | )\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\log \left| n \right|} \right). We show that if $\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\left( {{{\log \log \left| n \right|} \mathord{\left/
{\vphantom {{\log \log \left| n \right|} {\log \log \log \left| n \right|}}} \right.
\kern-\nulldelimiterspace} {\log \log \log \left| n \right|}}} \right)^{1/12} } \right)$\left\| {e^{in\phi } } \right\|_{A(\mathbb{T})} = o\left( {\left( {{{\log \log \left| n \right|} \mathord{\left/
{\vphantom {{\log \log \left| n \right|} {\log \log \log \left| n \right|}}} \right.
\kern-\nulldelimiterspace} {\log \log \log \left| n \right|}}} \right)^{1/12} } \right), then φ is linear. 相似文献
5.
Igor V. Protasov 《Algebra Universalis》2009,62(4):339-343
Let ${\mathbb{A}}Let
\mathbbA{\mathbb{A}} be a universal algebra of signature Ω, and let I{\mathcal{I}} be an ideal in the Boolean algebra
P\mathbbA{\mathcal{P}_{\mathbb{A}}} of all subsets of
\mathbbA{\mathbb{A}} . We say that I{\mathcal{I}} is an Ω-ideal if I{\mathcal{I}} contains all finite subsets of
\mathbbA{\mathbb{A}} and f(An) ? I{f(A^{n}) \in \mathcal{I}} for every n-ary operation f ? W{f \in \Omega} and every A ? I{A \in \mathcal{I}} . We prove that there are 22à0{2^{2^{\aleph_0}}} Ω-ideals in
P\mathbbA{\mathcal{P}_{\mathbb{A}}} provided that
\mathbbA{\mathbb{A}} is countably infinite and Ω is countable. 相似文献
6.
E. A. Sevost’yanov 《Ukrainian Mathematical Journal》2010,62(2):241-258
It is shown that if a point x
0 ∊ ℝ
n
, n ≥ 3, is an essential isolated singularity of an open discrete Q-mapping f : D →
[`(\mathbb Rn)] \overline {\mathbb {R}^n} , B
f
is the set of branch points of f in D; and a point z
0 ∊
[`(\mathbb Rn)] \overline {\mathbb {R}^n} is an asymptotic limit of f at the point x
0; then, for any neighborhood U containing the point x
0; the point z
0 ∊ [`(f( Bf ?U ))] \overline {f\left( {B_f \cap U} \right)} provided that the function Q has either a finite mean oscillation at the point x
0 or a logarithmic singularity whose order does not exceed n − 1: Moreover, for n ≥ 2; under the indicated conditions imposed on the function Q; every point of the set
[`(\mathbb Rn)] \overline {\mathbb {R}^n} \ f(D) is an asymptotic limit of f at the point x
0. For n ≥ 3, the following relation is true:
[`(\mathbbRn )] \f( D ) ì [`(f Bf )] \overline {\mathbb{R}^n } \backslash f\left( D \right) \subset \overline {f\,B_f } . In addition, if ¥ ? f( D ) \infty \notin f\left( D \right) , then the set f
B
f
is infinite and x0 ? [`(Bf )] x_0 \in \overline {B_f } . 相似文献
7.
Christophe Dupont 《Mathematische Annalen》2011,349(3):509-528
Let f be an endomorphism of
\mathbbC\mathbbPk{\mathbb{C}\mathbb{P}^k} and ν be an f-invariant measure with positive Lyapunov exponents (λ
1, . . . , λ
k
). We prove a lower bound for the pointwise dimension of ν in terms of the degree of f, the exponents of ν and the entropy of ν. In particular our result can be applied for the maximal entropy measure μ. When k = 2, it implies that the Hausdorff dimension of μ is estimated by dimHm 3 [(log d)/(l1)] + [(log d)/(l2)]{{\rm dim}_\mathcal{H}\mu \geq {{\rm log} d \over \lambda_1} + {{\rm log} d \over \lambda_2}}, which is half of the conjectured formula. Our method for proving these results consists in studying the distribution of
the ν-generic inverse branches of f
n
in
\mathbbC\mathbbPk{\mathbb{C}\mathbb{P}^k} . Our tools are a volume growth estimate for the bounded holomorphic polydiscs in
\mathbbC\mathbbPk{\mathbb{C}\mathbb{P}^k} and a normalization theorem for the ν-generic inverse branches of f
n
. 相似文献
8.
E. A. Sevost’yanov 《Ukrainian Mathematical Journal》2011,63(1):84-97
For open discrete mappings
f:D\{ b } ? \mathbbR3 f:D\backslash \left\{ b \right\} \to {\mathbb{R}^3} of a domain
D ì \mathbbR3 D \subset {\mathbb{R}^3} satisfying relatively general geometric conditions in D \ {b} and having an essential singularity at a point
b ? \mathbbR3 b \in {\mathbb{R}^3} , we prove the following statement: Let a point y
0 belong to
[`(\mathbbR3)] \f( D\{ b } ) \overline {{\mathbb{R}^3}} \backslash f\left( {D\backslash \left\{ b \right\}} \right) and let the inner dilatation K
I
(x, f) and outer dilatation K
O
(x, f) of the mapping f at the point x satisfy certain conditions. Let B
f
denote the set of branch points of the mapping f. Then, for an arbitrary neighborhood V of the point y
0, the set V ∩ f(B
f
) cannot be contained in a set A such that g(A) = I, where
I = { t ? \mathbbR:| t | < 1 } I = \left\{ {t \in \mathbb{R}:\left| t \right| < 1} \right\} and
g:U ? \mathbbRn g:U \to {\mathbb{R}^n} is a quasiconformal mapping of a domain
U ì \mathbbRn U \subset {\mathbb{R}^n} such that A ⊂ U. 相似文献
9.
Giovanni Di Lena Davide Franco Mario Martelli Basilio Messano 《Mediterranean Journal of Mathematics》2011,8(4):473-489
The main purpose of this paper is to investigate dynamical systems
F : \mathbbR2 ? \mathbbR2{F : \mathbb{R}^2 \rightarrow \mathbb{R}^2} of the form F(x, y) = (f(x, y), x). We assume that
f : \mathbbR2 ? \mathbbR{f : \mathbb{R}^2 \rightarrow \mathbb{R}} is continuous and satisfies a condition that holds when f is non decreasing with respect to the second variable. We show that for every initial condition x0 = (x
0, y
0), such that the orbit
O(x0) = {x0, x1 = F(x0), x2 = F(x1), . . . }, O({\rm{x}}_0) = \{{\rm{x}}_0, {\rm{x}}_1 = F({\rm{x}}_0), {\rm{x}}_2 = F({\rm{x}}_1), . . . \}, 相似文献
10.
Jae-Young Chung 《Aequationes Mathematicae》2012,83(3):313-320
Let \mathbb R{\mathbb R} be the set of real numbers, f : \mathbb R ? \mathbb R{f : \mathbb {R} \to \mathbb {R}}, e 3 0{\epsilon \ge 0} and d > 0. We denote by {(x 1, y 1), (x 2, y 2), (x 3, y 3), . . .} a countable dense subset of \mathbb R2{\mathbb {R}^2} and let
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