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1.
Yuming Liu 《Proceedings of the American Mathematical Society》2003,131(9):2657-2662
In this paper, we assume that algebras are finite dimensional algebras with 1 over a fixed field and modules over an algebra are finitely generated left unitary modules. Let and be two algebras (where is a splitting field for and ) with no semisimple summands. If two bimodules and induce a stable equivalence of Morita type between and , and if maps any simple -module to a simple -module, then is a Morita equivalence. This conclusion generalizes Linckelmann's result for selfinjective algebras. Our proof here is based on the construction of almost split sequences.
2.
Stephen J. Gardiner Mary Hanley 《Proceedings of the American Mathematical Society》2003,131(3):773-779
Let denote a relatively closed subset of the unit ball of . The purpose of this paper is to characterize those sets which have the following property: any harmonic function on which satisfies on (where 0$">) can be locally uniformly approximated on by a sequence of harmonic polynomials which satisfy the same inequality on . This answers a question posed by Stray, who had earlier solved the corresponding problem for holomorphic functions on the unit disc.
3.
Jü rgen Herzog Takayuki Hibi 《Proceedings of the American Mathematical Society》2003,131(9):2641-2647
Let be the polynomial ring in variables over a field and its graded maximal ideal. Let be homogeneous polynomials of degree generating an -primary ideal, and let be arbitrary homogeneous polynomials of degree . In the present paper it will be proved that the Castelnuovo-Mumford regularity of the standard graded -algebra is at most . By virtue of this result, it follows that the regularity of a simplicial semigroup ring with isolated singularity is at most , where is the multiplicity of and is the codimension of .
4.
Vadim Kostrykin Konstantin A. Makarov Alexander K. Motovilov 《Proceedings of the American Mathematical Society》2003,131(11):3469-3476
We discuss the problem of perturbation of spectral subspaces for linear self-adjoint operators on a separable Hilbert space. Let and be bounded self-adjoint operators. Assume that the spectrum of consists of two disjoint parts and such that 0$">. We show that the norm of the difference of the spectral projections
for and is less than one whenever either (i) or (ii) and certain assumptions on the mutual disposition of the sets and are satisfied.
for and is less than one whenever either (i) or (ii) and certain assumptions on the mutual disposition of the sets and are satisfied.
5.
A note on the spectrum of an upper triangular operator matrix 总被引:1,自引:0,他引:1
Mohamed Barraa Mohamed Boumazgour 《Proceedings of the American Mathematical Society》2003,131(10):3083-3088
Let be a upper triangular operator matrix acting on the Banach space . We investigate the set of the operators for which , where denotes the spectrum.
6.
Lucien Chevalier 《Proceedings of the American Mathematical Society》2003,131(3):933-936
Let denote the local time (at 0) associated with a martingale . The aim of this note is to prove that the mapping is continuous from into weak-.
7.
Fernando Etayo 《Proceedings of the American Mathematical Society》2003,131(9):2911-2920
In this note we define the measure of holomorphicness of a compact real submanifold of an almost Hermitian manifold . The number verifies the following properties: is a complex submanifold iff ; if is odd, then . Explicit examples of surfaces in are obtained, showing that and that , being the Clifford torus.
8.
Alexandre Turull 《Proceedings of the American Mathematical Society》2004,132(9):2563-2565
We observe a simple formula to compute the number of Hall -subgroups of a -separable finite group in terms of only the action of a fixed Hall -subgroup of on a set of normal -sections of . As a consequence, we obtain that divides whenever is a subgroup of a finite -separable group . This generalizes a recent result of Navarro. In addition, our method gives an alternative proof of Navarro's result.
9.
Let be a finite codimensional quasi-invariant subspace of the Fock space . Then there exists a polynomial such that . We show that generates if and only if for some .
10.
Rü diger Gö bel Warren May 《Proceedings of the American Mathematical Society》2003,131(9):2705-2710
Let be abelian groups where is a direct sum of countable -groups. A condition is given on the Ulm-Kaplansky -invariants of and such that .
11.
Sufficient conditions for one domain to contain another in a space of constant curvature 总被引:4,自引:0,他引:4
Jiazu Zhou 《Proceedings of the American Mathematical Society》1998,126(9):2797-2803
As an application of the analogue of C-S. Chen's kinematic formula in the 3-dimensional space of constant curvature , that is, Euclidean space , -sphere , hyperbolic space (, respectively), we obtain sufficient conditions for one domain to contain another domain in either an Euclidean space , or a -sphere or a hyperbolic space .
12.
Lin Chen Ruan Yingbin Yan Zikun 《Proceedings of the American Mathematical Society》2003,131(9):2753-2759
We prove that if are injective, then is subscalar if and only if is subscalar. As corollaries, it is shown that -hyponormal operators and log-hyponormal operators are subscalar; also w-hyponormal operators with Ker Kerand their generalized Aluthge transformations are subscalar.
13.
For orders and conjugacy in finite group theory, Lagrange's Theorem and the class equation have universal application. Here, the class equation (extended to monoids via standard group action by conjugation) is applied to factorizable submonoids of the symmetric inverse monoid. In particular, if is a monoid induced by a subgroup of the symmetric group , then the center (all elements of that commute with every element of ) is if and only if is transitive. In the case where is both transitive and of order either or (for prime), formulas are provided for the order of as well as the number and sizes of its conjugacy classes.
14.
Abdelbaki Boutabaa Alain Escassut 《Proceedings of the American Mathematical Society》1998,126(9):2557-2568
Let be a complete ultrametric algebraically closed field of characteristic zero, and let be the field of meromorphic functions in . For all set in and for all we denote by the subset of : zero of order After studying unique range sets for entire functions in in a previous article, here we consider a similar problem for meromorphic functions by showing, in particular, that, for every , there exist sets of elements in such that, if have the same poles (counting multiplicities), and satisfy , then . We show how to construct such sets.
15.
J. Berkovits 《Proceedings of the American Mathematical Society》2003,131(9):2963-2966
The imbedding theorem of Browder and Ton states that for any real separable Banach space there exist a real separable Hilbert space and a compact linear injection such that is dense in We shall give a short and elementary new proof to this result. We also briefly discuss the corresponding result without the completeness assumption.
16.
17.
Fangyan Lu 《Proceedings of the American Mathematical Society》2003,131(12):3883-3892
Let be a subalgebra of a nest algebra . If contains all rank one operators in , then is said to be large; if the set of rank one operators in coincides with that in the Jacobson radical of , is said to be radical-type. In this paper, algebraic isomorphisms of large subalgebras and of radical-type subalgebras are characterized. Let be a nest of subspaces of a Hilbert space and be a subalgebra of the nest algebra associated to (). Let be an algebraic isomorphism from onto . It is proved that is spatial if one of the following occurs: (1) () is large and contains a masa; (2) () is large and closed; (3) () is a closed radical-type subalgebra and ( is quasi-continuous (i.e. the trivial elements of are limit points); (4) () is large and one of and is not quasi-continuous.
18.
Thomas Schlumprecht Vladimir G. Troitsky 《Proceedings of the American Mathematical Society》2003,131(5):1405-1413
We show that C. J. Read's example of an operator on which does not have any non-trivial invariant subspaces is not the adjoint of an operator on a predual of . Furthermore, we present a bounded diagonal operator such that even though is unbounded, the operator is a bounded operator on with invariant subspaces, and is adjoint to an operator on .
19.
Seungsu Hwang 《Proceedings of the American Mathematical Society》2003,131(10):3221-3230
On a compact -dimensional manifold , a critical point of the total scalar curvature functional, restricted to the space of metrics with constant scalar curvature of volume 1, satisfies the critical point equation (CPE), given by . It has been conjectured that a solution of the CPE is Einstein. Restricting our considerations to and assuming that there exist at least two distinct solutions of the CPE throughout the paper, we first prove that, if the second homology of vanishes, then is diffeomorphic to (Theorem 2). Secondly, we prove that the same conclusion holds if we have a lower Ricci curvature bound or the connectedness of a certain surface of (Theorem 3). Finally, we also prove that, if two connected surfaces of are disjoint, is isometric to a standard -sphere (Theorem 4).
20.
Masaharu Kusuda 《Proceedings of the American Mathematical Society》2003,131(10):3075-3081
Let be a -algebra and let be a full (right) Hilbert -module. It is shown that if the spectrum of is discrete, then every closed --submodule of is complemented in , and conversely that if is a -space and if every closed --submodule of is complemented in , then is discrete.