共查询到20条相似文献,搜索用时 15 毫秒
1.
M.S. Moslehian 《Linear algebra and its applications》2009,430(4):1131-1987
We give an extension of Hua’s inequality in pre-Hilbert C∗-modules without using convexity or the classical Hua’s inequality. As a consequence, some known and new generalizations of this inequality are deduced. Providing a Jensen inequality in the content of Hilbert C∗-modules, another extension of Hua’s inequality is obtained. We also present an operator Hua’s inequality, which is equivalent to operator convexity of given continuous real function. 相似文献
2.
Sergei? Sergeev 《Linear algebra and its applications》2009,431(8):1325-1757
In max algebra it is well known that the sequence of max algebraic powers Ak, with A an irreducible square matrix, becomes periodic after a finite transient time T(A), and the ultimate period γ is equal to the cyclicity of the critical graph of A.In this connection, we study computational complexity of the following problems: (1) for a given k, compute a periodic power Ar with and r?T(A), (2) for a given x, find the ultimate period of {Al⊗x}. We show that both problems can be solved by matrix squaring in O(n3logn) operations. The main idea is to apply an appropriate diagonal similarity scaling A?X-1AX, called visualization scaling, and to study the role of cyclic classes of the critical graph. 相似文献
3.
We consider products of unitary operators with at most two points in their spectra, 1 and eiα. We prove that the scalar operator eiγI is a product of k such operators if α(1+1/(k-3))?γ?α(k-1-1/(k-3)) for k?5. Also we prove that for eiα≠-1, only a countable number of scalar operators can be decomposed in a product of four operators from the mentioned class. As a corollary we show that every unitary operator on an infinite-dimensional space is a product of finitely many such operators. 相似文献
4.
Let W and M be two finite dimensional subspaces of a Hilbert space H such that H=W⊕M⊥, and let PW‖M⊥ denote the oblique projection with range W and nullspace M⊥. In this article we get the following formula for the singular values of PW‖M⊥
5.
In this paper we are interested in the existence of solutions of the following initial value problem: on (0,T) with u(0)=u0 where A:V→V′ is a monotone operator, G:V→V′ is a nonlinear nonmonotone operator and f:(0,T)→V′ is a measurable function, by means of a recent generalization of the famous KKM-Fan’s lemma. 相似文献
6.
Using the arithmetic-geometric mean inequality, we give bounds for k-subpermanents of nonnegative n×n matrices F. In the case k=n, we exhibit an n2-set S whose arithmetic and geometric means constitute upper and lower bounds for per(F)/n!. We offer sharpened versions of these bounds when F has zero-valued entries. 相似文献
7.
The product of operators with closed range in Hilbert C-modules 总被引:1,自引:0,他引:1
K. Sharifi 《Linear algebra and its applications》2011,435(5):1122-1130
Suppose T and S are bounded adjointable operators with close range between Hilbert C∗-modules, then TS has closed range if and only if Ker(T)+Ran(S) is an orthogonal summand, if and only if Ker(S∗)+Ran(T∗) is an orthogonal summand. Moreover, if the Dixmier (or minimal) angle between Ran(S) and Ker(T)∩[Ker(T)∩Ran(S)]⊥ is positive and is an orthogonal summand then TS has closed range. 相似文献
8.
Philip Thijsse 《Integral Equations and Operator Theory》1997,27(2):228-251
In this paper we consider the following problem: Given two matricesA,Z∈? n×n , does there exist an invertiblen×n-matrixS such thatS ?1 AS is an upper triangular matrix andS ?1 ZS is a lower triangular matrix, and if so, what can be said about the order in which the eigenvalues ofA andZ appear on the diagonals of these triangular matrices? For special choices ofA andZ a complete solution is possible, as has been shown by several authors. Here we follow a lead, provided by Shmuel Friedland, who discussed the case where bothA andZ have at leastn-1 linearly independent eigenvectors, and we descibe the problem in terms of Jordan chains and left-Jordan chains for the matricesA, Z. The results give some insight in the question why certain classes of matrices (like the nonderogatory and the rank 1 matrices) allow for a detailed solution of the problems described above; for some of these classes the result of this analysis is presented here for the first time. 相似文献
9.
C. Costara 《Linear algebra and its applications》2011,435(11):2674-2680
Let T be a continuous map of the space of complex n×n matrices into itself satisfying T(0)=0 such that the spectrum of T(x)-T(y) is always a subset of the spectrum of x-y. There exists then an invertible n×n matrix u such that either T(a)=uau-1 for all a or T(a)=uatu-1 for all a. We arrive at the same conclusion by supposing that the spectrum of x-y is always a subset of the spectrum of T(x)-Tt(y), without the continuity assumption on T. 相似文献
10.
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
11.
Magdalena Wanat 《Linear algebra and its applications》2006,414(1):304-309
We generalize two results: Kraaijevanger’s 1991 characterization of diagonal stability via Hadamard products and the block matrix version of the closure of the positive definite matrices under Hadamard multiplication. We restate our generalizations in terms of Pα-matrices and α-scalar diagonally stable matrices. 相似文献
12.
Let H be a separable Hilbert space with an orthonormal basis {en/n∈N}, T be a bounded tridiagonal operator on H and Tn be its truncation on span ({e1, e2, … , en}). We study the operator equation Tx = y through its finite dimensional truncations Tnxn = yn. It is shown that if and are bounded, then T is invertible and the solution of Tx = y can be obtained as a limit in the norm topology of the solutions of its finite dimensional truncations. This leads to uniform boundedness of the sequence . We also give sufficient conditions for the boundedness of and in terms of the entries of the matrix of T. 相似文献
13.
Chun Yuan Deng 《Linear algebra and its applications》2010,432(4):847-856
In this paper, we investigate the set ω(P) of generalized quadratic operators A satisfying the equation A2=αA+βP for all complex numbers α and β and for an idempotent operator P such that AP=PA=A. Furthermore, the close relationship between the operator A∈ω(P) and the idempotent operator P are established and expressions for the inverse, the Moore-Penrose inverse and the Drazin inverse of A∈ω(P) are given. Some related results are also obtained. 相似文献
14.
Ádám Besenyei 《Linear algebra and its applications》2011,435(5):984-997
Some functions f:R+→R+ induce mean of positive numbers and the matrix monotonicity gives a possibility for means of positive definite matrices. Moreover, such a function f can define a linear mapping on matrices (which is basic in the constructions of monotone metrics). The present subject is to check the complete positivity of in the case of a few concrete functions f. This problem has been motivated by applications in quantum information. 相似文献
15.
Tetiana Budnitska 《Linear algebra and its applications》2011,434(2):582-592
We study affine operators on a unitary or Euclidean space U up to topological conjugacy. An affine operator is a map f:U→U of the form f(x)=Ax+b, in which A:U→U is a linear operator and b∈U. Two affine operators f and g are said to be topologically conjugate if g=h-1fh for some homeomorphism h:U→U.If an affine operator f(x)=Ax+b has a fixed point, then f is topologically conjugate to its linear part A. The problem of classifying linear operators up to topological conjugacy was studied by Kuiper and Robbin [Topological classification of linear endomorphisms, Invent. Math. 19 (2) (1973) 83-106] and other authors.Let f:U→U be an affine operator without fixed point. We prove that f is topologically conjugate to an affine operator g:U→U such that U is an orthogonal direct sum of g-invariant subspaces V and W,
- •
- the restriction g∣V of g to V is an affine operator that in some orthonormal basis of V has the form(x1,x2,…,xn)?(x1+1,x2,…,xn-1,εxn) 相似文献
16.
Peter S. Landweber 《Linear algebra and its applications》2009,431(8):1317-1324
The reformulation of the Bessis-Moussa-Villani (BMV) conjecture given by Lieb and Seiringer asserts that the coefficient αm,k(A,B) of tk in the polynomial Tr(A+tB)m, with A,B positive semidefinite matrices, is nonnegative for all m,k. We propose a natural extension of a method of attack on this problem due to Hägele, and investigate for what values of m,k the method is successful, obtaining a complete determination when either m or k is odd. 相似文献
17.
18.
Edward Hanson 《Linear algebra and its applications》2011,435(11):2961-2970
Let V denote a vector space with finite positive dimension. We consider an ordered pair of linear transformations A:V→V and A∗:V→V that satisfy (i) and (ii) below:
- (i)
- There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A∗ is diagonal.
- (ii)
- There exists a basis for V with respect to which the matrix representing A∗ is irreducible tridiagonal and the matrix representing A is diagonal.
19.
The main topic of the paper is best constants in Markov-type inequalities between the norms of higher derivatives of polynomials and the norms of the polynomials themselves. The norm is the L2 norm with Laguerre weight. The leading term of the asymptotics of the constants is determined and tight bounds for the principal coefficient in this term, which is the operator norm of a Volterra operator, are given. For best constants in inequalities of the Wirtinger type, the limit is computed and an asymptotic formula for the error term is presented. 相似文献
20.
Let T be a linear operator on the space of all m×n matrices over any field. we prove that if T maps rank-2 matrices to rank-2 matrices then there exist nonsingular matrices U and V such that either T(X)=UXV for all matrices X, or m=n and T(X)=UXtV for all matrices X where Xt denotes the transpose of X. 相似文献