共查询到20条相似文献,搜索用时 31 毫秒
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.
It is known [KRS] that for each finitely generated Banach algebra
there exists a numberN such that for eachn>N the matrix algebras
can be generated by three idempotents. In this paper we show that the same statement is true for direct sums
and
, where
is a finitely generated free algebra, i.e. polynomials in several non-commuting variables. These results are new even for
algebras
because the numberN we obtain here improves known estimates (see for example [R]). We show that the algebra
can be generated by two idempotents if and only ifn
j
=2 for eachj and
is singly generated. Also we give an example of a free singly generated algebra
for which
can not be generated by two idempotents. But% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn%
hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x%
fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacuWFSeIqgaacaaaa!409A!\[{\tilde
{\cal B}}\] can be generated by three idempotents for each singly generated free algebra
. 相似文献
3.
Let be a boolean function, and suppose that the spectral
norm
of f is at most M. Then where and each H
j
is a subgroup of . This result may be regarded as a quantitative analogue of the Cohen-Helson-Rudin structure theorem for idempotent measures
in locally compact abelian groups.
Received: May 2006 Accepted: January 2007 相似文献
4.
Shahar Mendelson Alain Pajor Nicole Tomczak-Jaegermann 《Geometric And Functional Analysis》2007,17(4):1248-1282
We present a randomized method to approximate any vector from a set . The data one is given is the set T, vectors of and k scalar products , where are i.i.d. isotropic subgaussian random vectors in , and . We show that with high probability, any for which is close to the data vector will be a good approximation of , and that the degree of approximation is determined by a natural geometric parameter associated with the set T.
We also investigate a random method to identify exactly any vector which has a relatively short support using linear subgaussian
measurements as above. It turns out that our analysis, when applied to {−1, 1}-valued vectors with i.i.d. symmetric entries,
yields new information on the geometry of faces of a random {−1, 1}-polytope; we show that a k- dimensional random {−1, 1}-polytope with n vertices is m-neighborly for
The proofs are based on new estimates on the behavior of the empirical process when F is a subset of the L
2 sphere. The estimates are given in terms of the γ
2 functional with respect to the ψ
2 metric on F, and hold both in exponential probability and in expectation.
Received: November 2005, Revision: May 2006, Accepted: June 2006 相似文献
5.
Let G be an additive subgroup of a normed space X. We say that a point is weakly separated (resp. -separated) from G if it can be separated from G by a continuous character (resp. by a continuous positive definite function). Let T : X → Y be a continuous linear operator. Consider the following conditions:
(ws) if , then x is weakly separated from G;
(ps) if , then x is -separated from G;
(wp) if Tx is -separated from T(G), then x is weakly separated from G.
By (resp. , ) we denote the class of operators T : X → Y which satisfy (ws) (resp. (ps), (wp)) for all and all subgroups G of X. The paper is an attempt to describe the above classes of operators for various Banach spaces X, Y. It is proved that if X, Y are Hilbert spaces, then is the class of Hilbert-Schmidt operators. It is also shown that if T is a Hilbert-to-Banach space operator with finite ℓ-norm, then .
相似文献
6.
F. E. A. Johnson 《Archiv der Mathematik》2008,90(2):123-132
A module J over a ring is said to be hyperstable when . Over a module M for which Ext we show that the projective n-stems for which is hyperstable constitute a single homotopy type.
Received: 17 November 2006 相似文献
7.
Miroslav Pavlović 《Czechoslovak Mathematical Journal》2008,58(4):1039-1043
For a C
1-function f on the unit ball ⊂ ℂ
n
we define the Bloch norm by , where is the invariant derivative of f, and then show that
.
Supported by MNZŽS Serbia, Project No. 144010. 相似文献
8.
Pier Domenico Lamberti Massimo Lanza de Cristoforis 《Mediterranean Journal of Mathematics》2007,4(4):435-449
Let Ω be an open connected subset of for which the imbedding of the Sobolev space W
1,2(Ω) into the space L
2(Ω) is compact. We consider the Neumann eigenvalue problem for the Laplace operator in the open subset (Ω) of , where is a Lipschitz continuous homeomorphism of Ω onto (Ω). Then we prove a result of real analytic dependence for symmetric functions of the eigenvalues upon variation of .
This paper represents an extension of a part of the work performed by P.D. Lamberti in his PhD Thesis at the University of
Padova under the guidance of M. Lanza de Cristoforis. 相似文献
9.
Sergiu Aizicovici Vasile Staicu 《NoDEA : Nonlinear Differential Equations and Applications》2007,14(3-4):361-376
We prove the existence of integral solutions to the nonlocal Cauchy problem in a Banach space X, where is m-accretive and such that –A generates a compact semigroup, has nonempty, closed and convex values, and is strongly-weakly upper semicontinuous with respect to its second variable,
and . The case when A depends on time is also considered.
相似文献
10.
Yonutz V. Stanchescu 《Combinatorica》2008,28(3):343-355
We describe the structure of three dimensional sets of lattice points, having a small doubling property. Let be a finite subset of ℤ3 such that dim = 3. If and , then lies on three parallel lines. Moreover, for every three dimensional finite set that lies on three parallel lines, if , then is contained in three arithmetic progressions with the same common difference, having together no more than terms. These best possible results confirm a recent conjecture of Freiman and cannot be sharpened by reducing the quantity
υ or by increasing the upper bounds for . 相似文献
11.
Stefan Gille 《Archiv der Mathematik》2007,88(4):333-343
Let
be a closed subscheme of the noetherian scheme X. We show that if X has a dualizing complex
then there exists a dualizing complex
of Z such that there is an isomorphism of coherent Witt groups
for all
.
Received: 3 March 2006 相似文献
12.
Chaohui ZHANG? 《数学年刊B辑(英文版)》2008,29(1):85-94
It is well known that certain isotopy classes of oseudo-Anosov maos on a Riemann surface S of non-excluded type can be defined through Dehn twists tα and tβ along simple closed geodesics α and β on S,respectively. Let G be the corresponding Fuchsian group acting on the hyperbolic plane H so that H/G≌S.For any point α∈S,define S = S/{α}.In this article, the author gives explicit parabolic elements of G from which he constructs pseudo-Anosov classes on S that can be projected to a given pseudo-Anosov class on S obtained from Thurston's construction. 相似文献
13.
V. D. Lyakhovsky 《Journal of Mathematical Sciences》2008,151(2):2907-2923
New solutions of twist equations for the universal enveloping algebras U (An−1) are found. These solutions can be represented as products of full chains of extended Jordanian twists Abelian factors (“rotations”) , and sets of quasi-Jordanian twists . The latter are generalizations of Jordanian twists (with carrier b2) for special deformed extensions of the Hopf algebra U (b2). The carrier subalgebra for the composition is a nonminimal parabolic subalgebra in A
n−1 such that . The parabolic twisting elements are obtained in an explicit form. Details of the construction are illustrated by considering the examples n = 4 and n = 11.
Bibliography: 21 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 347, 2007, pp. 187–213. 相似文献
14.
Application of the Trace Inequality to the Poisson Equation 总被引:1,自引:0,他引:1
Sadek Gala 《Positivity》2008,12(2):289-312
The purpose of this paper is to show that solutions of the Poisson equation
where f be a complex-valued distribution on , d ≥ 3 and satisfy the coercivity property : for all . The coercivity of this equation is well studied by Maz’ ya and Verbitsky [14] in the case where f belongs to the class of positive Borel measures.
相似文献
15.
Muneo Chō Mariko Giga Tadasi Huruya Takeaki Yamazaki 《Integral Equations and Operator Theory》2007,57(3):303-308
Let
be an invertible class A operator such that
. Then we show that
, where gT is the principal function of T. Moreover, we show that if T is pure, then
. 相似文献
16.
Michel Weber 《Results in Mathematics》2007,51(1-2):141-179
Let where are independent Bernoulli random variables. In relation with the divisor problem, we evaluate the almost sure asymptotic
order of the sums , where and is a sequence of positive integers.
Received: May 23, 2007. Revised: June 8, 2007. 相似文献
17.
Raúl E. Curto Lawrence A. Fialkow H. Michael Möller 《Integral Equations and Operator Theory》2008,60(2):177-200
For a degree 2n real d-dimensional multisequence to have a representing measure μ, it is necessary for the associated moment matrix to be positive semidefinite and for the algebraic variety associated to β, , to satisfy rank card as well as the following consistency condition: if a polynomial vanishes on , then . We prove that for the extremal case , positivity of and consistency are sufficient for the existence of a (unique, rank -atomic) representing measure. We also show that in the preceding result, consistency cannot always be replaced by recursiveness
of .
The first-named author’s research was partially supported by NSF Research Grants DMS-0099357 and DMS-0400741. The second-named
author’s research was partially supported by NSF Research Grant DMS-0201430 and DMS-0457138. 相似文献
18.
This paper deals with the solvability of the boundary value problem
where p ∈ (1, ∞) is fixed, is convex, proper, lower semicontinuous, is a Carathéodory mapping and .
Received: 12 February 2007 相似文献
19.
A CDCSL algebra is a reflexive operator algebra with completely distributive and commutative subspace lattice. In this paper,
we show, for a weakly closed linear subspace
of a CDCSL algebra
, that
is a Lie ideal if and only if
for all invertibles A in
, and that
is a Jordan ideal if and only if it is an associative ideal. 相似文献
20.
Liviu I. Ignat Julio D. Rossi 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(5):918-925
In this paper we study the asymptotic behaviour as t → ∞ of solutions to a nonlocal diffusion problem on a lattice, namely, with t ≥ 0 and . We assume that J is nonnegative and verifies . We find that solutions decay to zero as t → ∞ and prove an optimal decay rate using, as our main tool, the discrete Fourier transform.
相似文献