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1.
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.
2.
Monika Budzynska 《Proceedings of the American Mathematical Society》2003,131(9):2771-2777
If is the open unit ball in the Cartesian product furnished with the -norm , where and , then a holomorphic self-mapping of has a fixed point if and only if for some
3.
Craig J. Sutton 《Proceedings of the American Mathematical Society》2003,131(9):2933-2936
Let be the -sphere of constant positive curvature. For , we will show that a measure on the unit tangent bundle of , which is even and invariant under the geodesic flow, is not uniquely determined by its projection to .
4.
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 .
5.
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.
6.
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.
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8.
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.
9.
Fabio Nicola 《Proceedings of the American Mathematical Society》2003,131(9):2841-2848
We are concerned with the so-called -pseudo-differential calculus. We describe the spectrum of the unital and commutative -algebra given by the norm closure of the space of -order pseudo-differential operators modulo compact operators; other related algebras are also considered. Finally, their -theory is computed.
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.
Fernando Szechtman 《Proceedings of the American Mathematical Society》2003,131(12):3657-3664
We refer to an automorphism of a group as -inner if given any subset of with cardinality less than , there exists an inner automorphism of agreeing with on . Hence is 2-inner if it sends every element of to a conjugate. New examples are given of outer -inner automorphisms of finite groups for all natural numbers .
12.
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.
13.
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).
14.
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-.
15.
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.
16.
Gabriel Navarro 《Proceedings of the American Mathematical Society》2003,131(10):3019-3020
If is a finite group and is a prime number, let be the number of Sylow -subgroups of . If is a subgroup of a -solvable group , we prove that divides .
17.
Rü diger Gö bel Warren May 《Proceedings of the American Mathematical Society》2003,131(10):2987-2992
Under the assumptions of MA and CH, it is proved that if is a field of prime characteristic and is an -separable abelian -group of cardinality , then an isomorphism of the group algebras and implies an isomorphism of and .
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19.
Hong Bing Yu 《Proceedings of the American Mathematical Society》2003,131(9):2639-2640
By using Scherk's lemma we give a simple combinatorial proof of a theorem due to Bollobás and Leader. For any sequence of elements of an abelian group of order , calling the sum of terms of the sequence a -sum, if 0 is not a -sum, then there are at least -sums.
20.
Zhongwei Shen 《Proceedings of the American Mathematical Society》2003,131(11):3447-3456
Let be a noncompact complete Riemannian manifold. We consider the Schrödinger operator acting on , where is a nonnegative, locally integrable function on . We obtain some simple conditions which imply that , the bottom of the spectrum of , is strictly positive. We also establish upper and lower bounds for the counting function .