If and are linear operators acting between Banach spaces, we show that compactness of relative to does not in general imply that has -bound zero. We do, however, give conditions under which the above implication is valid.
Let be the Iwasawa decomposition of a complex connected semi-simple Lie group . Let be a parabolic subgroup containing , and let be its commutator subgroup. In this paper, we characterize the -invariant Kähler structures on , and study the holomorphic sections of their corresponding pre-quantum line bundles.
Suppose is a block of a group algebra with cyclic defect group. We calculate the Hochschild cohomology ring of , giving a complete set of generators and relations. We then show that if is the principal block, the canonical map from to the Hochschild cohomology ring of induces an isomorphism modulo radicals. 相似文献
Let be an imaginary abelian number field. We know that , the relative class number of , goes to infinity as , the conductor of , approaches infinity, so that there are only finitely many imaginary abelian number fields with given relative class number. First of all, we have found all imaginary abelian number fields with relative class number one: there are exactly 302 such fields. It is known that there are only finitely many CM-fields with cyclic ideal class groups of 2-power orders such that the complex conjugation is the square of some automorphism of . Second, we have proved in this paper that there are exactly 48 such fields.
If is a co-Frobenius Hopf algebra over a field, having a Galois -object which is separable over , its ring of coinvariants, then is finite dimensional.
Let be a -finite measure space and let be a Frobenius-Perron operator.
In 1997 Bartoszek and Brown proved that if overlaps supports and if there exists , 0$"> on , such that , then is (strongly) asymptotically stable.
In the note we prove that instead of assuming that 0$"> on , it is enough to assume that and . More precisely, we prove that is asymptotically stable if and only if overlaps supports and there exists , , , such that .
It is shown that a set-valued mapping of a hyperconvex metric space which takes values in the space of nonempty externally hyperconvex subsets of always has a lipschitzian single valued selection which satisfies for all . (Here denotes the usual Hausdorff distance.) This fact is used to show that the space of all bounded -lipschitzian self-mappings of is itself hyperconvex. Several related results are also obtained.
Let be a rank two Chevalley group and be the corresponding Moufang polygon. J. Tits proved that is the universal completion of the amalgam formed by three subgroups of : the stabilizer of a point of , the stabilizer of a line incident with , and the stabilizer of an apartment passing through and . We prove a slightly stronger result, in which the exact structure of is not required. Our result can be used in conjunction with the ``weak -pair" theorem of Delgado and Stellmacher in order to identify subgroups of finite groups generated by minimal parabolics.
Let be a Douglas algebra and let be its Bourgain algebra. It is proved that admits a codimension 1 linear isometry if and only if . This answers the conjecture of Araujo and Font.
On bounded domains we consider the anisotropic problems in with 1$"> and on and in with and on . Moreover, we generalize these boundary value problems to space-dimensions 2$">. Under geometric conditions on and monotonicity assumption on we prove existence and uniqueness of positive solutions. 相似文献
Let be the unit disk. We show that for some relatively closed set there is a function that can be uniformly approximated on by functions of , but such that cannot be written as , with and uniformly continuous on . This answers a question of Stray.