共查询到20条相似文献,搜索用时 11 毫秒
1.
R. Drnovšek D. Kokol-Bukovšek L. Livshits G. MacDonald M. Omladič H. Radjavi 《Integral Equations and Operator Theory》2002,42(4):449-460
We construct an irreducible multiplicative semigroup of non-negative square-zero operators acting onL
p
[0,1), for 1p<.The main idea for this paper was developed at the 2nd Linear Algebra Workshop at Bled, Slovenia, in June 1999.The work of the three Slovenian authors was supported by the Research Ministry of Slovenia.This author's work was supported by a Division grant from Colby College. 相似文献
2.
Yuan-Chuan Li 《Linear algebra and its applications》2008,428(10):2319-2323
We study the joint spectral radius given by a finite set of compact operators on a Hilbert space. It is shown that the normed finiteness property holds in this case, that is, if all the compact operators are contractions and the joint spectral radius is equal to 1 then there exists a finite product that has a spectral radius equal to 1. We prove an additional statement in that the requirement that the joint spectral radius be equal to 1 can be relaxed to the asking that the maximum norm of finite products of a length norm is equal to 1. The length of this product is related to the dimension of the subspace on which the set of operators is norm preserving. 相似文献
3.
T. Hara 《Integral Equations and Operator Theory》1995,23(2):179-204
A bounded linear operatorT is a numerical contraction if and only if there exists a selfadjoint contractionZ such that
. The aim of the present paper is to study the structure of the coreZ(T) of all selfadjoint contractions satisfying the above inequality. Especially we consider several conditions for thatZ(T) is a single-point set. By using this argument we shall characterize extreme points of the set of all numerical contractions. Moreover we shall give effective sufficient conditions for extreme points. 相似文献
4.
We study various aspects of how certain positivity assumptions on complex matrix semigroups affect their structure. Our main result is that every irreducible group of complex matrices with nonnegative diagonal entries is simultaneously similar to a group of weighted permutations. We also consider the corresponding question for semigroups and discuss the effect of the assumption that a fixed linear functional has nonnegative values when restricted to a given semigroup. 相似文献
5.
Sang-Gu Lee 《Linear algebra and its applications》2011,435(9):2097-2109
We investigate simultaneous solutions of the matrix Sylvester equations AiX-XBi=Ci,i=1,2,…,k, where {A1,…,Ak} and {B1,…,Bk} are k-tuples of commuting matrices of order m×m and p×p, respectively. We show that the matrix Sylvester equations have a unique solution X for every compatible k-tuple of m×p matrices {C1,…,Ck} if and only if the joint spectra σ(A1,…,Ak) and σ(B1,…,Bk) are disjoint. We discuss the connection between the simultaneous solutions of Sylvester equations and related questions about idempotent matrices separating disjoint subsets of the joint spectrum, spectral mapping for the differences of commuting k-tuples, and a characterization of the joint spectrum via simultaneous solutions of systems of linear equations. 相似文献
6.
Maria Inez Cardoso Gonçalves Ahmed Ramzi Sourour 《Linear algebra and its applications》2008,429(7):1478-1488
For 0<q<1, the q-numerical range is defined on the algebra Mn of all n×n complex matrices by
Wq(A)={x∗Ay:x,y∈Cn,∥x∥=∥y∥=1,〈y,x〉=q}. 相似文献
7.
Bamdad R. Yahaghi 《Linear algebra and its applications》2008,428(4):1151-1168
In this paper we consider collections of compact (resp. Cp class) operators on arbitrary Banach (resp. Hilbert) spaces. For a subring R of reals, it is proved that an R-algebra of compact operators with spectra in R on an arbitrary Banach space is triangularizable if and only if every member of the algebra is triangularizable. It is proved that every triangularizability result on certain collections, e.g., semigroups, of compact operators on a complex Banach (resp. Hilbert) space gives rise to its counterpart on a real Banach (resp. Hilbert) space. We use our main results to present new proofs as well as extensions of certain classical theorems (e.g., those due to Kolchin, McCoy, and others) on arbitrary Banach (resp. Hilbert) spaces. 相似文献
8.
Roman Drnovšek 《Integral Equations and Operator Theory》2001,39(3):253-266
Let
be a collection of bounded operators on a Banach spaceX of dimension at least two. We say that
is finitely quasinilpotent at a vectorx
0X whenever for any finite subset
of
the joint spectral radius of
atx
0 is equal 0. If such collection
contains a non-zero compact operator, then
and its commutant
have a common non-trivial invariant, subspace. If in addition,
is a collection of positive operators on a Banach lattice, then
has a common non-trivial closed ideal. This result and a recent remarkable theorem of Turovskii imply the following extension of the famous result of de Pagter to semigroups. Let
be a multiplicative semigroup of quasinilpotent compact positive operators on a Banach lattice of dimension at least two. Then
has a common non-trivial invariant closed ideal.This work was supported by the Research Ministry of Slovenia. 相似文献
9.
We show that the section determinant of eA can be expressed, under
certain conditions, by the Fredholm determinant of an integral operator. The
kernel function of this integral operator is computed explicitly in terms of the
operator A. As a simple consequence we derive a Weierstrass type product
expansion for the section determinant. 相似文献
10.
Clément de Seguins Pazzis 《Linear algebra and its applications》2011,435(11):2708-2721
Let (K) be a field. Given an arbitrary linear subspace V of Mn(K) of codimension less than n-1, a classical result states that V generates the (K)-algebra Mn(K). Here, we strengthen this statement in three ways: we show that Mn(K) is spanned by the products of the form AB with (A,B)∈V2; we prove that every matrix in Mn(K) can be decomposed into a product of matrices of V; finally, when V is a linear perplane of Mn(K) and n>2, we show that every matrix in Mn(K) is a product of two elements of V. 相似文献
11.
Masatoshi Fujii 《Linear algebra and its applications》2010,432(10):2565-640
We point out a sharp reverse Cauchy-Schwarz/Hölder matrix inequality. The Cauchy-Schwarz version involves the usual matrix geometric mean: Let Ai and Bi be positive definite matrices such that 0<mAi?Bi?MAi for some scalars 0<m?M and i=1,2,?,n. Then
12.
We give a matrix version of the scalar inequality f(a + b) ? f(a) + f(b) for positive concave functions f on [0, ∞). We show that Choi’s inequality for positive unital maps and operator convex functions remains valid for monotone convex functions at the cost of unitary congruences. Some inequalities for log-convex functions are presented and a new arithmetic-geometric mean inequality for positive matrices is given. We also point out a simple proof of the Bhatia-Kittaneh arithmetic-geometric mean inequality. 相似文献
13.
Let Mn be the algebra of all n×n matrices, and let φ:Mn→Mn be a linear mapping. We say that φ is a multiplicative mapping at G if φ(ST)=φ(S)φ(T) for any S,T∈Mn with ST=G. Fix G∈Mn, we say that G is an all-multiplicative point if every multiplicative linear bijection φ at G with φ(In)=In is a multiplicative mapping in Mn, where In is the unit matrix in Mn. We mainly show in this paper the following two results: (1) If G∈Mn with detG=0, then G is an all-multiplicative point in Mn; (2) If φ is an multiplicative mapping at In, then there exists an invertible matrix P∈Mn such that either φ(S)=PSP-1 for any S∈Mn or φ(T)=PTtrP-1 for any T∈Mn. 相似文献
14.
Hongyan Zeng 《Linear algebra and its applications》2011,434(2):463-474
Let A be a Banach algebra with unity I and M be a unital Banach A-bimodule. A family of continuous additive mappings D=(δi)i∈N from A into M is called a higher derivable mapping at X, if δn(AB)=∑i+j=nδi(A)δj(B) for any A,B∈A with AB=X. In this paper, we show that D is a Jordan higher derivation if D is a higher derivable mapping at an invertible element X. As an application, we also get that every invertible operator in a nontrivial nest algebra is a higher all-derivable point. 相似文献
15.
Jorge Antezana Gustavo Corach Demetrio Stojanoff 《Integral Equations and Operator Theory》2006,55(2):169-188
If
$$\mathcal{H}$$ is a Hilbert space,
$$\mathcal{S}$$ is a closed subspace of
$$\mathcal{H},$$ and A is a positive bounded linear operator on
$$\mathcal{H},$$ the spectral shorted operator
$$\rho \left( {\mathcal{S},\mathcal{A}} \right)$$ is defined as the infimum of the sequence
$$\sum (\mathcal{S},A^n )^{1/n} ,$$ where denotes
$$\sum \left( {\mathcal{S},B} \right)$$ the shorted operator of B to
$$\mathcal{S}.$$ We characterize the left spectral resolution of
$$\rho \left( {\mathcal{S},\mathcal{A}} \right)$$ and show several properties of this operator, particularly in the case that
dim
$${\mathcal{S} = 1.}$$ We use these results to generalize the concept of Kolmogorov complexity for the infinite dimensional
case and for non invertible operators. 相似文献
16.
We study error bounds in the operator norm topology for the Trotter-Kato product formula. We prove that they depend on fractional power conditions (domains and relative boundedness) for operators involved in this formula.Dedicated to Professor M.Sh.BIRMAN on the occassion of his 70th birthday. 相似文献
17.
We give some new examples of bounded multilinear forms on the Hilbert spaces ℓ2 and L2 (0, ∞). We characterize those which are compact or Hilbert-Schmidt. In particular, we study m-linear forms (m ≥ 3) on ℓ2 which can be regarded as the multilinear analogue of the famous Hilbert matrix. We also determine the norm of the permanent
on
where
相似文献
18.
19.
Let A and B be bounded linear operators acting on a Hilbert space H. It is shown that the triangular inequality serves as the ultimate estimate of the upper norm bound for the sum of two operators in the sense that
sup{∥U*AU+V*BV∥:U and V are unitaries}=min{∥A+μI∥+∥B-μI∥:μ∈C}. 相似文献
20.
Jagjit Singh Matharu Mohammad Sal Moslehian Jaspal Singh Aujla 《Linear algebra and its applications》2011,435(2):270-276
We present a weak majorization inequality and apply it to prove eigenvalue and unitarily invariant norm extensions of a version of the Bohr’s inequality due to Vasi? and Ke?ki?. 相似文献