共查询到20条相似文献,搜索用时 62 毫秒
1.
Let A be a unital algebra and M be a unital A-bimodule. A linear map δ : A →M is said to be Jordan derivable at a nontrivial idempotent P ∈ A if δ(A) ? B + A ? δ(B) =δ(A ? B) for any A, B ∈ A with A ? B = P, here A ? B = AB + BA is the usual Jordan product. In this article, we show that if A = Alg N is a Hilbert space nest algebra and M = B(H), or A = M = B(X), then, a linear map δ : A → M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P ∈ B(X) if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained. 相似文献
2.
3.
4.
Let be an extension of commutative rings with identity, X an analytic indeterminate over B, and , the subring of the formal power series ring , consisting of the series with constant terms in A. In this Note we study when the ring R is Noetherian. We prove that R is Noetherian if and only if A is Noetherian and B is a finitely generated A-module. To cite this article: S. Hizem, A. Benhissi, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
5.
Hyoung Joon Kim 《Journal of Mathematical Analysis and Applications》2012,386(1):110-114
It is well known that if , where A is compact, then T has a nontrivial hyperinvariant subspace. In this paper, we try to solve the hyperinvariant subspace problem for operators which have a compact part. Our main result is that if A is compact, then either or has a nontrivial hyperinvariant subspace. 相似文献
6.
Zhidong Pan 《Linear algebra and its applications》2012,436(11):4251-4260
7.
8.
9.
In this paper, we give sufficient conditions for a graph to have degree bounded trees. Let G be a connected graph and . We denote by the minimum value of the degree sum in G of any k pairwise nonadjacent vertices of A, and by the number of components of the subgraph of G induced by . Our main results are the following: (i) If , then G contains a tree T with maximum degree ⩽k and . (ii) If , then G contains a spanning tree T with for any . These are generalizations of the result by S. Win [S. Win, Existenz von Gerüsten mit Vorgeschriebenem Maximalgrad in Graphen, Abh. Math. Seminar Univ. Humburg 43 (1975) 263–267] and degree conditions are sharp. 相似文献
10.
11.
This work is concerned with the relations between exact controllability and complete stabilizability for linear systems in Hilbert spaces. We give an affirmative answer to the open problem posed by Rabah and Karrakchou [R. Rabah, J. Karrakchou, Exact controllability and complete stabilizability for linear systems in Hilbert spaces, Appl. Math. Lett. 10 (1997) 35–40]. More precisely, if the -semigroup generated by is surjective and the pair with a bounded operator is completely stabilizable, then is exactly controllable without any additional condition. 相似文献
12.
The Cauchy-Davenport theorem states that, if p is prime and A, B are nonempty subsets of cardinality r, s in , the cardinality of the sumset is bounded below by ; moreover, this lower bound is sharp. Natural extensions of this result consist in determining, for each group G and positive integers , the analogous sharp lower bound, namely the function Important progress on this topic has been achieved in recent years, leading to the determination of for all abelian groups G. In this note we survey the history of earlier results and the current knowledge on this function. 相似文献
13.
B.A. Sethuraman 《Journal of Pure and Applied Algebra》2018,222(11):3538-3546
Matrices A and B in are said to be mutually orthogonal if , where ? denotes the conjugate transpose. We study cardinalities of certain -linearly independent families of matrices arising from matrix embeddings of a division algebra of index m with center a number field Z, satisfying the property that matrices from different families are mutually orthogonal. The question is of importance in the context of coding for certain wireless channels, where the cardinalities of such sets is connected to the maximum code rate consistent with low decoding complexity. It follows from our results that the maximum code rate for the codes we consider is severely limited. 相似文献
14.
15.
16.
17.
Heybetkulu Mustafayev 《Comptes Rendus Mathematique》2006,342(8):575-578
Let be a bounded -semigroup on a Banach space with generator A. We define as the closure with respect to the operator-norm topology of the set , where is the Laplace transform of with respect to the semigroup T. Then is a commutative Banach algebra. It is shown that if the unitary spectrum of A is at most countable, then the Gelfand transform of vanishes on if and only if, . Some applications to the semisimplicity problem are given. To cite this article: H. Mustafayev, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
18.
19.
Let D be a commutative domain with field of fractions K, let A be a torsion-free D-algebra, and let B be the extension of A to a K-algebra. The set of integer-valued polynomials on A is , and the intersection of with is , which is a commutative subring of . The set may or may not be a ring, but it always has the structure of a left -module.A D-algebra A which is free as a D-module and of finite rank is called -decomposable if a D-module basis for A is also an -module basis for ; in other words, if can be generated by and A. A classification of such algebras has been given when D is a Dedekind domain with finite residue rings. In the present article, we modify the definition of -decomposable so that it can be applied to D-algebras that are not necessarily free by defining A to be -decomposable when is isomorphic to . We then provide multiple characterizations of such algebras in the case where D is a discrete valuation ring or a Dedekind domain with finite residue rings. In particular, if D is the ring of integers of a number field K, we show that an -decomposable algebra A must be a maximal D-order in a separable K-algebra B, whose simple components have as center the same finite unramified Galois extension F of K and are unramified at each finite place of F. Finally, when both D and A are rings of integers in number fields, we prove that -decomposable algebras correspond to unramified Galois extensions of K. 相似文献