共查询到20条相似文献,搜索用时 31 毫秒
1.
Mohammad Sal Moslehian 《Expositiones Mathematicae》2012,30(4):376-388
First, we take a historical glimpse at some significant refinements and extensions of the Kantorovich inequality. Second, we present some operator Kantorovich inequalities involving unital positive linear mappings and the operator geometric mean in the framework of semi-inner product C∗-modules and give some new and classical results in a unified approach. 相似文献
2.
Topological uniform descent and Weyl type theorem 总被引:1,自引:0,他引:1
Xiaohong Cao 《Linear algebra and its applications》2007,420(1):175-182
The generalized Weyl’s theorem holds for a Banach space operator T if and only if T or T∗ has the single valued extension property in the complement of the Weyl spectrum (or B-Weyl spectrum) and T has topological uniform descent at all λ which are isolated eigenvalues of T. Also, we show that the generalized Weyl’s theorem holds for analytically paranormal operators. 相似文献
3.
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
4.
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
5.
Mohammad Sal Moslehian 《Linear algebra and its applications》2011,434(8):1981-1987
We establish several operator versions of the classical Aczél inequality. One of operator versions deals with the weighted operator geometric mean and another is related to the positive sesquilinear forms. Some applications including the unital positive linear maps on C*-algebras and the unitarily invariant norms on matrices are presented. 相似文献
6.
B.P. Duggal 《Linear algebra and its applications》2006,414(1):271-277
A Banach space operator T is polaroid and satisfies Weyl’s theorem if and only if T is Kato type at points λ ∈ iso σ(T) and has SVEP at points λ not in the Weyl spectrum of T. For such operators T, f(T) satisfies Weyl’s theorem for every non-constant function f analytic on a neighborhood of σ(T) if and only if f(T∗) satisfies Weyl’s theorem. 相似文献
7.
B.P. Duggal 《Linear algebra and its applications》2007,422(1):331-340
A Hilbert space operator A ∈ B(H) is said to be p-quasi-hyponormal for some 0 < p ? 1, A ∈ p − QH, if A∗(∣A∣2p − ∣A∗∣2p)A ? 0. If H is infinite dimensional, then operators A ∈ p − QH are not supercyclic. Restricting ourselves to those A ∈ p − QH for which A−1(0) ⊆ A∗-1(0), A ∈ p∗ − QH, a necessary and sufficient condition for the adjoint of a pure p∗ − QH operator to be supercyclic is proved. Operators in p∗ − QH satisfy Bishop’s property (β). Each A ∈ p∗ − QH has the finite ascent property and the quasi-nilpotent part H0(A − λI) of A equals (A − λI)-1(0) for all complex numbers λ; hence f(A) satisfies Weyl’s theorem, and f(A∗) satisfies a-Weyl’s theorem, for all non-constant functions f which are analytic on a neighborhood of σ(A). It is proved that a Putnam-Fuglede type commutativity theorem holds for operators in p∗ − QH. 相似文献
8.
It is proved that the operator Lie algebra ε(T,T∗) generated by a bounded linear operator T on Hilbert space H is finite-dimensional if and only if T=N+Q, N is a normal operator, [N,Q]=0, and dimA(Q,Q∗)<+∞, where ε(T,T∗) denotes the smallest Lie algebra containing T,T∗, and A(Q,Q∗) denotes the associative subalgebra of B(H) generated by Q,Q∗. Moreover, we also give a sufficient and necessary condition for operators to generate finite-dimensional semi-simple Lie algebras. Finally, we prove that if ε(T,T∗) is an ad-compact E-solvable Lie algebra, then T is a normal operator. 相似文献
9.
S.W. Drury 《Linear algebra and its applications》2011,435(2):323-329
We present an effective algorithm for estimating the norm of an operator mapping a low-dimensional ?p space to a Banach space with an easily computable norm. We use that algorithm to show that Matsaev’s proposed extension of the inequality of John von Neumann is false in case p=4. Matsaev conjectured that for every contraction T on Lp (1<p<∞) one has for any polynomial P
‖P(T)‖Lp→Lp?‖P(S)‖?p(Z+)→?p(Z+) 相似文献
10.
Alexander Alldridge 《Advances in Mathematics》2008,218(1):163-201
We study the multivariate generalisation of the classical Wiener-Hopf algebra, which is the C∗-algebra generated by the Wiener-Hopf operators, given by convolutions restricted to convex cones. By the work of Muhly and Renault, this C∗-algebra is known to be isomorphic to the reduced C∗-algebra of a certain restricted action groupoid. It admits a composition series, and therefore, a ‘symbol’ calculus. Using groupoid methods, we obtain, in the framework of Kasparov's bivariant KK-theory, a topological expression of the index maps associated to these symbol maps in terms of geometric-topological data of the underlying convex cone. This generalises an index theorem by Upmeier concerning Wiener-Hopf operators on symmetric cones. Our result covers a wide class of cones containing polyhedral and homogeneous cones. 相似文献
11.
The main purpose of this paper is to study the continuity of several kinds of generalized inverses of elements in a Banach algebra with identity. We first obtain a sufficient and necessary condition for the lower semi-continuity of reflexive generalized inverses as set-valued mappings. Based on this result, we characterize the continuity of the Moore-Penrose inverse in a C∗-algebra and therefore, derive some new and well-known criteria in operator theory. 相似文献
12.
B.P. Duggal 《Linear algebra and its applications》2008,428(4):1109-1116
A Hilbert space operator A∈B(H) is p-hyponormal, A∈(p-H), if |A∗|2p?|A|2p; an invertible operator A∈B(H) is log-hyponormal, A∈(?-H), if log(TT∗)?log(T∗T). Let dAB=δAB or ?AB, where δAB∈B(B(H)) is the generalised derivation δAB(X)=AX-XB and ?AB∈B(B(H)) is the elementary operator ?AB(X)=AXB-X. It is proved that if A,B∗∈(?-H)∪(p-H), then, for all complex λ, , the ascent of (dAB-λ)?1, and dAB satisfies the range-kernel orthogonality inequality ‖X‖?‖X-(dAB-λ)Y‖ for all X∈(dAB-λ)-1(0) and Y∈B(H). Furthermore, isolated points of σ(dAB) are simple poles of the resolvent of dAB. A version of the elementary operator E(X)=A1XA2-B1XB2 and perturbations of dAB by quasi-nilpotent operators are considered, and Weyl’s theorem is proved for dAB. 相似文献
13.
Ivo Klemeš 《Linear algebra and its applications》2007,422(1):164-185
We study determinant inequalities for certain Toeplitz-like matrices over C. For fixed n and N ? 1, let Q be the n × (n + N − 1) zero-one Toeplitz matrix with Qij = 1 for 0 ? j − i ? N − 1 and Qij = 0 otherwise. We prove that det(QQ∗) is the minimum of det(RR∗) over all complex matrices R with the same dimensions as Q satisfying ∣Rij∣ ? 1 whenever Qij = 1 and Rij = 0 otherwise. Although R has a Toeplitz-like band structure, it is not required to be actually Toeplitz. Our proof involves Alexandrov’s inequality for polarized determinants and its generalizations. This problem is motivated by Littlewood’s conjecture on the minimum 1-norm of N-term exponential sums on the unit circle. We also discuss polarized Bazin-Reiss-Picquet identities, some connections with k-tree enumeration, and analogous conjectured inequalities for the elementary symmetric functions of QQ∗. 相似文献
14.
Markus Haase 《Positivity》2007,11(1):57-68
We prove pointwise convexity (Jensen-type) inequalities of the form Open image in new window where F is a convex function defined on a convex subset of some Banach space X and T is the X-valued extension of a positive operator on some function space. Examples include the pointwise Hölder inequality T(fg) ≤ (Tf p )1/ p (Tf q )1/ q for a positive sublinear operator T. As applications we consider vector-valued conditional expectation and a ``real'' proof of the Riesz-Thorin theorem for positive operators. 相似文献
15.
Jean-Christophe Bourin 《Linear algebra and its applications》2006,413(1):212-217
We review some recent convexity results for Hermitian matrices and we add a new one to the list: Let A be semidefinite positive, let Z be expansive, Z∗Z?I, and let f:[0,∞)→[0,∞) be a concave function. Then, for all symmetric norms
‖f(Z∗AZ)‖?‖Z∗f(A)Z‖. 相似文献
16.
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
17.
Wen Zhang 《Linear algebra and its applications》2011,435(6):1326-1335
Let A and B be (not necessarily unital or closed) standard operator algebras on complex Banach spaces X and Y, respectively. For a bounded linear operator A on X, the peripheral spectrum σπ(A) of A is the set σπ(A)={z∈σ(A):|z|=maxω∈σ(A)|ω|}, where σ(A) denotes the spectrum of A. Assume that Φ:A→B is a map the range of which contains all operators of rank at most two. It is shown that the map Φ satisfies the condition that σπ(BAB)=σπ(Φ(B)Φ(A)Φ(B)) for all A,B∈A if and only if there exists a scalar λ∈C with λ3=1 and either there exists an invertible operator T∈B(X,Y) such that Φ(A)=λTAT-1 for every A∈A; or there exists an invertible operator T∈B(X∗,Y) such that Φ(A)=λTA∗T-1 for every A∈A. If X=H and Y=K are complex Hilbert spaces, the maps preserving the peripheral spectrum of the Jordan skew semi-triple product BA∗B are also characterized. Such maps are of the form A?UAU∗ or A?UAtU∗, where U∈B(H,K) is a unitary operator, At denotes the transpose of A in an arbitrary but fixed orthonormal basis of H. 相似文献
18.
Shuxuan Li 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(11):3716-3727
In this paper, taking the Hessian Sobolev inequality (0<p≤k) (X.-J. Wang, 1994 [2]) as the starting point, we give a proof of the Hessian Sobolev inequality when k<p≤k∗, where k∗ is the critical Sobolev embedding index of k-Hessian type. We also prove that k∗ is optimal by one-dimensional Hardy’s inequality. 相似文献
19.
Masayoshi Kaneda 《Journal of Functional Analysis》2007,251(1):346-359
Let X be an operator space, let φ be a product on X, and let (X,φ) denote the algebra that one obtains. We give necessary and sufficient conditions on the bilinear mapping φ for the algebra (X,φ) to have a completely isometric representation as an algebra of operators on some Hilbert space. In particular, we give an elegant geometrical characterization of such products by using the Haagerup tensor product. Our result makes no assumptions about identities or approximate identities. Our proof is independent of the earlier result of Blecher, Ruan and Sinclair [D.P. Blecher, Z.-J. Ruan, A.M. Sinclair, A characterization of operator algebras, J. Funct. Anal. 89 (1) (1990) 188-201] which solved the case when the bilinear mapping has an identity of norm one, and our result is used to give a simple direct proof of this earlier result. We also develop further the connections between quasi-multipliers of operator spaces and their representations on a Hilbert space or their embeddings in the second dual, and show that the quasi-multipliers of operator spaces defined in [M. Kaneda, V.I. Paulsen, Quasi-multipliers of operator spaces, J. Funct. Anal. 217 (2) (2004) 347-365] coincide with their C∗-algebraic counterparts. 相似文献
20.
A complex number λ is an extended eigenvalue of an operator A if there is a nonzero operator X such that AX = λ XA. We characterize the set of extended eigenvalues, which we call extended point spectrum, for operators acting on finite dimensional
spaces, finite rank operators, Jordan blocks, and C0 contractions. We also describe the relationship between the extended eigenvalues of an operator A and its powers. As an application, we show that the commutant of an operator A coincides with that of An, n ≥ 2, n ∈ N if the extended point spectrum of A does not contain any n–th root of unity other than 1. The converse is also true if either A or A* has trivial kernel. 相似文献