共查询到20条相似文献,搜索用时 0 毫秒
1.
In this paper we ask which norms on Md induced by an absolute vector norm are sub-multiplicative with respect to the Hadamard product. We provide a simple necessary condition for submultiplicativity. We demonstrate that each norm on Md induced by an lp norm Hadamard submultiplicative and that the norms induced by certain polyhedral norms are Hadamard submultiplicative. We also consider some related inequalities. 相似文献
2.
In this paper we ask which norms on Md induced by an absolute vector norm are sub-multiplicative with respect to the Hadamard product. We provide a simple necessary condition for submultiplicativity. We demonstrate that each norm on Md induced by an lp norm Hadamard submultiplicative and that the norms induced by certain polyhedral norms are Hadamard submultiplicative. We also consider some related inequalities. 相似文献
3.
Heydar Radjavi Peter Rosenthal 《Proceedings of the American Mathematical Society》2007,135(1):163-168
It is shown that a transitive, closed, homogeneous semigroup of linear transformations on a finite-dimensional space either has zero divisors or is simultaneously similar to a group consisting of scalar multiples of unitary transformations. The proof begins with the result that for each closed homogeneous semigroup with no zero divisors there is a such that the spectral radius satisfies for all and in the semigroup.
It is also shown that the spectral radius is not -submultiplicative on any transitive semigroup of compact operators.
4.
The paper contains some general theorems for Hadamard product of matrices which in particular include Fiedler's Theorem and a better bound for an inequality on product of eigenvalues of certain matrices due to Ando. Lieb's concavity Theorem has been proved using operator means. Some inequalities for unitarily invariant norms have also been proved. 相似文献
5.
The paper contains some general theorems for Hadamard product of matrices which in particular include Fiedler's Theorem and a better bound for an inequality on product of eigenvalues of certain matrices due to Ando. Lieb's concavity Theorem has been proved using operator means. Some inequalities for unitarily invariant norms have also been proved. 相似文献
6.
7.
Thomas H. Pate 《Linear algebra and its applications》1976,14(3):285-292
Suppose each of m, n, and k is a positive integer, k ? n, A is a (real-valued) symmetric n-linear function on Em, and B is a k-linear symmetric function on Em. The tensor and symmetric products of A and B are denoted, respectively, by A ?B and A?B. The identity is proven by Neuberger in [1]. An immediate consequence of this identity is the inequality In this paper a necessary and sufficient condition for is given. It is also shown that under certain conditions the inequality can be considerably improved. This improvement results from an analysis of the terms 6A?qB6, 1?q?n, appearing in the identity. 相似文献
8.
In this paper we continue to study the spectral norms and their completions ([4]) in the case of the algebraic closure $ \overline {\mathbb Q} $ of ? in ?. Let $ \widetilde{\overline{\mathbb{Q}}} $ be the completion of $ \overline {\mathbb Q} $ relative to the spectral norm. We prove that $ \widetilde{\overline{\mathbb{Q}}} $ can be identified with the R‐subalgebra of all symmetric functions of C(G), where C(G) denotes the ?‐Banach algebra of all continuous functions defined on the absolute Galois group G = Gal$ {\overline {\mathbb Q}} / {\mathbb Q} $. We prove that any compact, closed to conjugation subset of ? is the pseudo‐orbit of a suitable element of $ \widetilde{\overline{\mathbb{Q}}} $. We also prove that the topological closure of any algebraic number field in $ \widetilde{\overline{\mathbb{Q}}} $ is of the form $\widetilde{\mathbb{Q}[x]}$ with x in $ \widetilde{\overline{\mathbb{Q}}} $. 相似文献
9.
Xingzhi Zhan 《Linear and Multilinear Algebra》2000,47(2):191-194
We pose some problems on the Hadamard product and singular values of matrices. 相似文献
10.
C.-S. Lin 《Proceedings of the American Mathematical Society》1999,127(6):1693-1696
The paper gives a necessary and sufficient condition for the norm equality of bounded linear operators and . The invertibility of an operator which is related to the norm equality is discussed. Some new results about the unilateral shift are given.
11.
Chandler Davis 《Numerische Mathematik》1962,4(1):343-344
12.
We describe the algebraic structure of linearly recursive sequences under the Hadamard (point-wise) product. We characterize
the invertible elements and the zero divisors. Our methods use the Hopf-algebraic structure of this algebra and classical
results on Hopf algebras. We show that our criterion for invertibility is effective if one knows a linearly recursive relation
for a sequence and certain information about finitely-generated subgroups of the multiplicitive group of the field.
Supported in part by NSF Grant DMS 870-1085. 相似文献
13.
Xingzhi Zhan 《Linear and Multilinear Algebra》2013,61(2):191-194
We pose some problems on the Hadamard product and singular values of matrices. 相似文献
14.
If A ∘ X is the Schur product of n×n matrices A and X, then we study estimates on the norm of the map X ↦ A ∘ X, where X has the norm it acquires as a linear operator on a complex n-dimensional Hilbert space. 相似文献
15.
Takaaki Nomura 《Journal of Functional Analysis》2003,198(1):229-267
In this paper, we present a geometric norm equality involving an admissible linear form ω for the Shilov boundary of a homogeneous Siegel domain D. We prove that the validity of this norm equality is equivalent to the symmetry of D and the reduction of ω essentially to the Koszul form. This, in particular, reveals a geometric reason that the Poisson kernel is annihilated by the Laplace-Beltrami operator if and only if D is symmetric, a theorem due to Hua, Look, Korányi and Xu. 相似文献
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17.
Mathematical Notes - In this paper, both well-known and new properties of the spectral abscissa and the logarithmic norm are described. In addition to well-known formulas for the norm of a matrix... 相似文献
18.
M. K. Aouf T. M. Seoudy 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2013,48(6):297-309
In this paper we obtain sandwich type theorems, inclusion relationships, convolution properties and coefficient estimates of certain classes of p-valent analytic functions defined by a convolution. Several other new results are also obtained. 相似文献
19.
C. Bení tez Manuel Ferná ndez Marí a L. Soriano 《Proceedings of the American Mathematical Society》1999,127(5):1437-1441
Real inner product spaces are characterized by the points at which the homogeneous 2-polynomials that are products of equal-norm linear functionals attain their norm.