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1.
Let T = U|T| be the polar decomposition of a bounded linear operator T on a Hilbert space. The transformation T = |T|^1/2 U|T|^1/2 is called the Aluthge transformation and Tn means the n-th Aluthge transformation. Similarly, the transformation T(*)=|T*|^1/2 U|T*|&1/2 is called the *-Aluthge transformation and Tn^(*) means the n-th *-Aluthge transformation. In this paper, firstly, we show that T(*) = UV|T^(*)| is the polar decomposition of T(*), where |T|^1/2 |T^*|^1/2 = V||T|^1/2 |T^*|^1/2| is the polar decomposition. Secondly, we show that T(*) = U|T^(*)| if and only if T is binormal, i.e., [|T|, |T^*|]=0, where [A, B] = AB - BA for any operator A and B. Lastly, we show that Tn^(*) is binormal for all non-negative integer n if and only if T is centered, and so on. 相似文献
2.
Atsushi Uchiyama 《Integral Equations and Operator Theory》1999,33(2):221-230
For an-multicyclicp-hyponormal operatorT, we shall show that |T|2p
–|T
*|2p
belongs to the Schatten
and that tr
Area ((T)). 相似文献
3.
Let T be a bounded linear
operator on a complex Hilbert space H.
T $/in$ B(H)
is called a log-hyponormal operator if T
is invertible and log (TT
*) log (T
*
T).
Since a function log : (0,) (-,) is operator
monotone, every invertible p-hyponormal operator T, i.e., (TT
*)
p
(T
*
T
p
is log-hyponormal for 0 < p 1. Putnams inequality for p-hyponormal operator
T is the following:$ \| (T^*T)^p-(TT^*)^p \|\leq\frac{p}{\pi}\int\int_{\sigma(T)}r^{2p-1}drd\theta $.In this paper, we prove that if T is log-hyponormal, then$ \| log(T^*T)-log(TT^*) \|\leq\frac{1}{\pi}\int\int_{\sigma(T)}r^{-1}drd\theta $. 相似文献
4.
Ariyadasa Aluthge 《Integral Equations and Operator Theory》1996,24(4):497-501
A bounded linear operatorT is calledp-Hyponormal if (T
*T)p(TT
*)p, 0<p1. In Aluthge [1], we studied the properties of p-hyponormal operators using the operator
. In this work we consider a more general operator
, and generalize some properties of p-hyponormal operators obtained in [1]. 相似文献
5.
Lucien Chevalier 《Probability Theory and Related Fields》1979,49(3):249-255
Summary We prove the following extension of classical Burkholder-Davis-Gundy inequalities: let (X
n
)
nN
be a martingale; for p1, in order that
and
belong to L
p, it is sufficient that Inf(X
*, S(X)) belong to L
p. For «regular» martingales this result holds for p>0. 相似文献
6.
Aleksandar Ivić 《Central European Journal of Mathematics》2004,2(4):494-508
Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of
. If
with
, then we obtain
. We also show how our method of proof yields the bound
, where T
1/5+ε≤G≪T, T<t
1<...<t
R
≤2T, t
r
+1−t
r
≥5G (r=1, ..., R−1). 相似文献
7.
Natalie M. Priebe 《Geometriae Dedicata》2000,79(3):239-265
In this paper, a technique for analyzing levels of hierarchy in a tiling
of Euclidean space is presented. Fixing a central configuration P of tiles in
, a `derived Voronoï' tessellation
P is constructed based on the locations of copies of P in
. A family of derived Voronoï tilings
is formed by allowing the central configurations to vary through an infinite number of possibilities. The family
will normally be an infinite one, but we show that for a self-similar tiling
it is finite up to similarity. In addition, we show that if the family
is finite up to similarity, then
is pseudo-self-similar. The relationship between self-similarity and pseudo-self-similarity is not well understood, and this is the obstruction to a complete characterization of self-similarity via our method. A discussion and conjecture on the connection between the two forms of hierarchy for tilings is provided. 相似文献
8.
We prove that there exists a series of the form (*)
, where {nk(x)} is a subsystem of either the trigonometric or the Walsh system such that
; where n as n and for each > 0 a weight function (x) can be constructed such that 0 < (x) 1,
, and series (*) is universal in the space L1
with respect simultaneously to rearrangements as well as to subseries. 相似文献
9.
Aleksandar Ivić 《Monatshefte für Mathematik》1987,104(1):17-27
The existence of zeros ofZ
(k)(t) in short intervals of the type [T, T+H] is established, whereHT
a(k)logT,
. Hitherto the sharpest bounds for the constanta(k) are obtained by employing a certain exponential averaging technique and the estimation of the relevant exponential sums. Bounds for
are also derived, under the assumption that
orZ(t) does not vanish in certain short intervals. 相似文献
10.
We obtain new unimprovable Kolmogorov-type inequalities for differentiable periodic functions. In particular, we prove that, for r = 2, k = 1 or r = 3, k = 1, 2 and arbitrary q, p [1, ], the following unimprovable inequality holds for functions
:
where
and
r
is the perfect Euler spline of order r. 相似文献
11.
Given a real sequence {n}n. Suppose that
is a frame for L2[–, ] with bounds A, B. The problem is to find a positive constant L such that for any real sequence {n}n with ¦n –n¦ <L,
is also a frame for L2[–, ]. Balan [1] obtained
arcsin
. This value is a good stability bound of Fourier frames because it covers Kadec's 1/4-theorem
and is better than
(see Duffin and Schaefer [3]). In this paper, a sharper estimate is given. 相似文献
12.
Define the operator of Sunouchi
(f L
1) on the Walsh group with respect to the Walsh-Kaczmarz system. In this paper we prove that the operator T
is of weak type (1, 1), of type (H
1, L
1) and of type (p, p) for all 1 < p 2. 相似文献
13.
A linear operatorT L(H) is called a strongly irreducible, if there is no non-trivial idempotent linear operator commuting withT. In this paper, denote the set of all strongly irreducible operators by (SI). Let
be a nest with infinite dimensional atoms,
be the nest algebra associated with
and
be the closure of
, then the following result is proved
.The projection partially supported by Chinese Natural Science Foundation and Fund of Laboratory of Nonlinear Mathematical Modeling and Methods in Fudan University in Shanghai P.R.C. 相似文献
14.
Let
be realhomogeneous functions in
ofdegree
and let bethe Borel measure on
given by
where dx denotes theLebesgue measure on
and > 0. Let T
be the convolution operator
and let
Assume that, for x 0, the followingtwo conditions hold:
vanishes only at h = 0 and
. In this paper we show that if
then E
is the empty set and if
then E
is the closed segment withendpoints
and
. Also, we give some examples. 相似文献
15.
N. L. Vasilevski 《Integral Equations and Operator Theory》1999,34(1):107-126
Let
be the unit disk in,
be the Bergman space, consisting of all analytic functions from
, and
be the Bergman projection of
onto
. We constructC
*-algebras
, for functions of which the commutator of Toeplitz operators [T
a
,T
b
]=T
a
T
b
–T
b
T
a
is compact, and, at the same time, the semi-commutator [T
a
,T
b
)=T
a
T
b
–T
ab
is not compact.It is proved, that for each finite set =n
0,n
1, ...,n
m
, where 1=n
0
1
<...
m
, andn
k
{}, there are algebras
of the above type, such that the symbol algebras Sym
of Toeplitz operator algebras
arecommutative, while the symbol algebras Sym
of the algebras
, generated by multiplication operators
and
, haveirreducible representations exactly of dimensions n
0,n
1,..., n
m
.This work was partially supported by CONACYT Project 3114P-E9607, México. 相似文献
16.
Palle E. T. Jorgensen 《Integral Equations and Operator Theory》1999,35(2):125-171
This paper is devoted to an approximation problem for operators in Hilbert space, that appears when one tries to study geometrically thecascade algorithm in wavelet theory. Let
be a Hilbert space, and let be a representation ofL
(
) on
. LetR be a positive operator inL
(
) such thatR(1) =1, where1 denotes the constant function 1. We study operatorsM on
(bounded, but noncontractive) such that
where the * refers to Hilbert space adjoint. We give a complete orthogonal expansion of
which reduces such thatM acts as a shift on one part, and the residual part is
() =
n
[M
n
], where [M
n
] is the closure of the range ofM
n
. The shift part is present, we show, if and only if ker (M
*){0}. We apply the operator-theoretic results to the refinement operator (or cascade algorithm) from wavelet theory. Using the representation , we show that, for this wavelet operatorM, the components in the decomposition are unitarily, and canonically, equivalent to spacesL
2(E
n
) L
2(), whereE
n , n=1,2,3,..., , are measurable subsets which form a tiling of ; i.e., the union is up to zero measure, and pairwise intersections of differentE
n
's have measure zero. We prove two results on the convergence of the cascale algorithm, and identify singular vectors for the starting point of the algorithm.Terminology used in the paper
the one-torus
-
Haar measure on the torus
-
Z
the Zak transform
-
X=ZXZ
–1
transformation of operators
-
a given Hilbert space
-
a representation ofL
(
) on
-
R
the Ruelle operator onL
(
)
-
M
an operator on
-
R
*,M
*
adjoint operators
Work supported in part by the U.S. National Science Foundation. 相似文献
17.
Let n
i
,m
j
> 1. In [5], the sperical noncommutative torus
was defined by twisting
in
by a totally skew multiplier p on
for T
pd
a pd-homogeneous C*-algebra over
. It is shown that
is strongly Morita equivalent to
.
This work is supported by Grant No. 1999-2-102-001-3 from the interdisciplinary research program year of the KOSEF 相似文献
18.
Milutin Dostanić 《Czechoslovak Mathematical Journal》1999,49(4):707-732
We find an exact asymptotic formula for the singular values of the integral operator of the form
, a Jordan measurable set) where
and L is slowly varying function with some additional properties. The formula is an explicit expression in terms of L and T. 相似文献
19.
In the open disk
of the complex plane, we consider the following spaces of functions: the Bloch space
; the Hardy--Sobolev space
; and the Hardy--Besov space
. It is shown that if all the poles of the rational function R of degree n,
, lie in the domain
, then
, where
and
depends only on
. The second of these inequalities for the case of the half-plane was obtained by Semmes in 1984. The proof given by Semmes was based on the use of Hankel operators, while our proof uses the special integral representation of rational functions. 相似文献
20.
Takuya Hara 《Integral Equations and Operator Theory》1992,15(4):551-567
Let
be a Hilbert space. A continuous positive operatorT on
uniquely determines a Hilbert space
which is continuously imbedded in
and for which
with the canonical imbedding
. A Kreîn space version of this result, however, is not valid in general. This paper provides a necessary and sufficient condition for that a continuous selfadjoint operatorT uniquely determines a Kreîn space (
) which is continuously imbedded in
and for which
with the canonical imbedding
. 相似文献