共查询到20条相似文献,搜索用时 109 毫秒
1.
Let be an -dimensional space of linear operators between the linear spaces and over an algebraically closed field . Improving results of Larson, Ding, and Li and Pan we show the following.
Theorem. Let be a basis of . Assume that every nonzero operator in has rank larger than . Then a linear operator belongs to if and only if for every , is a linear combination of .
2.
Let be the set of all linear transformations from to , where and are vector spaces over a field . We show that every -dimensional subspace of is algebraically -reflexive, where denotes the largest integer not exceeding , provided is less than the cardinality of .
3.
Raymond Mortini 《Proceedings of the American Mathematical Society》2007,135(6):1795-1801
Let be the Banach algebra of all bounded analytic functions in the unit disk . A function is said to be universal with respect to the sequence of noneuclidian translates, if the set is locally uniformly dense in the set of all holomorphic functions bounded by . We show that for any sequence of points in tending to the boundary there exists a closed subspace of , topologically generated by Blaschke products, and linear isometric to , such that all of its elements are universal with respect to noneuclidian translates. The proof is based on certain interpolation problems in the corona of . Results on cyclicity of composition operators in are deduced.
4.
José Carlos Sierra Andrea Luigi Tironi 《Proceedings of the American Mathematical Society》2007,135(5):1263-1269
We classify smooth complex projective varieties of dimension admitting a divisor of the form among their hyperplane sections, both and of codimension in their respective linear spans. In this setting, one of the following holds: 1) is either the Veronese surface in or its general projection to , 2) and is contained in a quadric cone of rank or , 3) and .
5.
For spaces on , and , sharp versions of the classical Marchaud inequality are known. These results are extended here to Orlicz spaces (on , and ) for which is convex for some , , where is the Orlicz function. Sharp converse inequalities for such spaces are deduced.
6.
Henrik Petersson 《Proceedings of the American Mathematical Society》2007,135(4):1145-1149
A sequence of operators is said to be hypercyclic if there exists a vector , called hypercyclic for , such that is dense. A hypercyclic subspace for is a closed infinite-dimensional subspace of, except for zero, hypercyclic vectors. We prove that if is a sequence of operators on that has a hypercyclic subspace, then there exist (i) a sequence of one variable polynomials such that is hypercyclic for every fixed and (ii) an operator that maps nonzero vectors onto hypercyclic vectors for .
We complement earlier work of several authors.
7.
Srikanth Iyengar Tony J. Puthenpurakal 《Proceedings of the American Mathematical Society》2007,135(3):637-648
For a finitely generated, non-free module over a CM local ring , it is proved that for the length of is given by a polynomial of degree . The vanishing of is studied, with a view towards answering the question: If there exists a finitely generated -module with such that the projective dimension or the injective dimension of is finite, then is regular? Upper bounds are provided for beyond which the question has an affirmative answer.
8.
S. Rohde 《Proceedings of the American Mathematical Society》2007,135(4):1169-1173
In this note, we provide an answer to a question of D. Mejia and Chr. Pommerenke, by constructing a hyperbolically convex subdomain of the unit disc so that the conformal map from to maps a set of dimension 0 on to a set of dimension
9.
Ugur Madran 《Proceedings of the American Mathematical Society》2007,135(4):987-995
Let be a finite group of order divisible by a prime acting on an vector space where is the field with elements and . Consider the diagonal action of on copies of This note sharpens a lower bound for for groups which have an element of order whose Jordan blocks have sizes at most 2.
10.
We study the complexification of real Hilbert -modules over real -algebras. We give an example of a Hilbert -module that is not the complexification of any Hilbert -module, where is a real -algebra.
11.
Gene Freudenburg 《Proceedings of the American Mathematical Society》2007,135(1):51-57
A family of -actions on affine space is constructed, each having a non-finitely generated ring of invariants (). Because these actions are of small degree, they induce linear actions of unipotent groups on for , and these invariant rings are also non-finitely generated. The smallest such action presented here is for the group acting linearly on .
12.
Christopher J. Hillar Lionel Levine 《Proceedings of the American Mathematical Society》2007,135(6):1607-1618
Let be an algebraically closed field of characteristic zero and let . The -th cyclic resultant of is
Res
A generic monic polynomial is determined by its full sequence of cyclic resultants; however, the known techniques proving this result give no effective computational bounds. We prove that a generic monic polynomial of degree is determined by its first cyclic resultants and that a generic monic reciprocal polynomial of even degree is determined by its first of them. In addition, we show that cyclic resultants satisfy a polynomial recurrence of length . This result gives evidence supporting the conjecture of Sturmfels and Zworski that resultants determine . In the process, we establish two general results of independent interest: we show that certain Toeplitz determinants are sufficient to determine whether a sequence is linearly recurrent, and we give conditions under which a linearly recurrent sequence satisfies a polynomial recurrence of shorter length. 13.
The cascade algorithm plays an important role in computer graphics and wavelet analysis. For an initial function , a cascade sequence is constructed by the iteration where is defined by In this paper, under a condition that the sequence is bounded in , we prove that the following three statements are equivalent: (i) converges . (ii) For , there exist a positive constant and a constant such that (iii) For some converges in . An example is presented to illustrate our result.
14.
Jens Heber Gerhard Knieper Hemangi M. Shah 《Proceedings of the American Mathematical Society》2007,135(3):845-849
Let be a Hadamard manifold of dimension whose sectional curvature satisfies and whose curvature tensor satisfies for suitable constants and . We show that is of constant sectional curvature provided is asymptotically harmonic. This was previously only known if admits a compact quotient.
15.
Yifeng Xue 《Proceedings of the American Mathematical Society》2007,135(3):705-711
A unital -algebra is said to have the (APD)-property if every nonzero element in has the approximate polar decomposition. Let be a closed ideal of . Suppose that and have (APD). In this paper, we give a necessary and sufficient condition that makes have (APD). Furthermore, we show that if and or is a simple purely infinite -algebra, then has (APD).
16.
Ta Thi Hoai An 《Proceedings of the American Mathematical Society》2007,135(5):1255-1261
If is a non-Archimedean analytic curve in a projective variety embedded in and if are hypersurfaces of in general position with then we prove the defect relation:
17.
Alvaro Pelayo 《Proceedings of the American Mathematical Society》2007,135(1):277-288
We compute the homotopy type of the space of -equivariant symplectic embeddings from the standard -dimensional ball of some fixed radius into a -dimensional symplectic-toric manifold , and use this computation to define a -valued step function on which is an invariant of the symplectic-toric type of . We conclude with a discussion of the partially equivariant case of this result.
18.
Alec Matheson 《Proceedings of the American Mathematical Society》2007,135(5):1335-1341
A closed set in the unit circle is the boundary spectrum of a uniform Frostman Blaschke product if and only if is nowhere dense in .
19.
David Schrittesser 《Proceedings of the American Mathematical Society》2007,135(4):1213-1222
-absoluteness for forcing means that for any forcing , . `` inaccessible to reals' means that for any real , . To measure the exact consistency strength of `` -absoluteness for forcing and is inaccessible to reals', we introduce a weak version of a weakly compact cardinal, namely, a (lightface) -indescribable cardinal; has this property exactly if it is inaccessible and .
20.
S. Prashanth 《Proceedings of the American Mathematical Society》2007,135(1):201-209
Let denote the closure of in the norm Let and define the constants and Let We consider the following problem for We show an exact multiplicity result for for all small .