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1.
Let be a -group with generator , and let be a local -semigroup commuting with . Then the operators , , form a local -semigroup. It is proved that if is injective and is the generator of , then is closable and is the generator of . Also proved are a characterization theorem for local -semigroups with not necessarily injective and a theorem about solvability of the abstract inhomogeneous Cauchy problem:
2.
Mohsen Pourahmadi Akihiko Inoue Yukio Kasahara 《Proceedings of the American Mathematical Society》2007,135(4):1233-1239
For a nonnegative integrable weight function on the unit circle , we provide an expression for , in terms of the series coefficients of the outer function of , for the weighted distance , where is the normalized Lebesgue measure and ranges over trigonometric polynomials with frequencies in , , . The problem is open for .
3.
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 .
4.
Guangxing Zeng 《Proceedings of the American Mathematical Society》2007,135(4):929-938
The purpose of this paper is to investigate the interplay between henselian valuations and orderings (or semiorderings) of a ring. As a main result, it is proved that for a henselian valuation on a ring , the following statements are equivalent: (1) is compatible with every semiordering of ; (2) is compatible with every ordering of ; (3) Every real prime ideal of is contained in the core of .
5.
Alexander J. Izzo 《Proceedings of the American Mathematical Society》2007,135(4):1065-1071
Let denote the open unit disc, and let denote the disc algebra. The subsets of such that the inclusion holds for every nonconstant continuous on , or the inclusion holds for every bounded harmonic nonholomorphic function on continuous on , are characterized. In the first case the condition is that has positive measure, and in the second case that has full measure in .
6.
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.
7.
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.
8.
Given a perfect field of characteristic , a smooth proper -scheme , a crystal on relative to and a finite group acting on and , we show that, viewed as a virtual -module, the reduction modulo of the crystalline cohomology of is the de Rham cohomology of modulo . On the way we prove a base change theorem for the virtual -representations associated with -equivariant objects in the derived category of -modules.
9.
Nicolas Burq Andrew Hassell Jared Wunsch 《Proceedings of the American Mathematical Society》2007,135(4):1029-1037
We consider Dirichlet eigenfunctions of the Bunimovich stadium , satisfying . Write where is the central rectangle and denotes the ``wings,' i.e., the two semicircular regions. It is a topic of current interest in quantum theory to know whether eigenfunctions can concentrate in as . We obtain a lower bound on the mass of in , assuming that itself is -normalized; in other words, the norm of is controlled by times the norm in . Moreover, if is an quasimode, the same result holds, while for an quasimode we prove that the norm of is controlled by times the norm in . We also show that the norm of may be controlled by the integral of along , where is a smooth factor on vanishing at . These results complement recent work of Burq-Zworski which shows that the norm of is controlled by the norm in any pair of strips contained in , but adjacent to .
10.
Takateru Okayasu Yasunori Ueta 《Proceedings of the American Mathematical Society》2007,135(5):1399-1403
We will give some sufficient conditions for a -hyponormal operator, , to be normal, and a sufficient condition for a triplet of operators , , with , self-adjoint and unitary such that necessarily satisfies .
11.
Bruce A. Barnes 《Proceedings of the American Mathematical Society》2007,135(6):1735-1740
Let be a bounded linear operator on a Banach space and let be a subspace of which is a Banach space and invariant. Denote by the restriction of to This paper explores the questions:
If the range of is closed, under what conditions is the range of closed?
If the range of is closed, under what conditions is the range of closed?
12.
Walter Ferrer Santos Alvaro Rittatore 《Proceedings of the American Mathematical Society》2007,135(4):961-968
In this paper we axiomatize some constructions and results due to Cayley and Hilbert. We define the concept of -process for an arbitrary affine algebraic monoid with zero and unit group . In our situation we show how to produce from the process and for a linear rational representation of a number of elements of the ring of -invariants that is large enough to guarantee its finite generation. Moreover, using complete reducibility, we give an explicit construction of all -processes for reductive monoids.
13.
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
14.
Margarida Mendes Lopes Rita Pardini 《Proceedings of the American Mathematical Society》2007,135(5):1279-1282
In this note it is shown that, given a smooth minimal complex surface of general type with , , for which the bicanonical map is a morphism, the degree of is not 3. This completes our earlier results, showing that if is a minimal surface of general type with , such that is free, then the bicanonical map of can have degree 1, 2 or 4.
15.
Florin Panaite Freddy Van Oystaeyen 《Proceedings of the American Mathematical Society》2007,135(6):1669-1677
If is a quasi-Hopf algebra and is a right -comodule algebra such that there exists a morphism of right -comodule algebras, we prove that there exists a left -module algebra such that . The main difference when comparing to the Hopf case is that, from the multiplication of , which is associative, we have to obtain the multiplication of , which in general is not; for this we use a canonical projection arising from the fact that becomes a quasi-Hopf -bimodule.
16.
Mariagrazia Bianchi David Chillag Mark L. Lewis Emanuele Pacifici 《Proceedings of the American Mathematical Society》2007,135(3):671-676
Let be a finite group, and write for the set of degrees of irreducible characters of . We define to be the graph whose vertex set is , and there is an edge between and if . We prove that if is a complete graph, then is a solvable group.
17.
Jorge Mujica Paula Takatsuka 《Proceedings of the American Mathematical Society》2007,135(4):1141-1144
We show that if is a starlike domain in a Banach space and is a family of holomorphic functions on that omit two distinct values and is bounded at the origin, then is uniformly bounded on each -bounded set.
18.
Birol Altin 《Proceedings of the American Mathematical Society》2007,135(4):1059-1063
Schmidt proved that an operator from a Banach lattice into a Banach lattice with property is order bounded if and only if its adjoint is order bounded, and in this case satisfies . In the present paper the result is generalized to Banach lattices with Levi-Fatou norm serving as range, and some characterizations of Banach lattices with a Levi norm are given. Moreover, some characterizations of Riesz spaces having property are also obtained.
19.
Albin L. Jones 《Proceedings of the American Mathematical Society》2007,135(4):1197-1204
Consider an arbitrary partition of the triples of all countable ordinals into two classes. We show that either for each finite ordinal the first class of the partition contains all triples from a set of type , or for each finite ordinal the second class of the partition contains all triples of an -element set. That is, we prove that for each pair of finite ordinals and .
20.
Rodney Y. Sharp 《Proceedings of the American Mathematical Society》2007,135(3):665-670
Let be a commutative Noetherian local ring of prime characteristic. The purpose of this paper is to provide a short proof of G. Lyubeznik's extension of a result of R. Hartshorne and R. Speiser about a module over the skew polynomial ring (associated to and the Frobenius homomorphism , in the indeterminate ) that is both -torsion and Artinian over .