Let be a -uniformly smooth Banach space possessing a weakly sequentially continuous duality map (e.g., ). Let be a Lipschitzian pseudocontractive selfmapping of a nonempty closed convex and bounded subset of and let be arbitrary. Then the iteration sequence defined by , converges strongly to a fixed point of , provided that and have certain properties. If is a Hilbert space, then converges strongly to the unique fixed point of closest to .
Let be a certain Banach space consisting of continuous functions defined on the open unit disk. Let be a univalent function defined on , and assume that denotes the operator of multiplication by . We characterize the structure of the operator such that . We show that for some function in . We also characterize the commutant of under certain conditions.
1. If and is nilpotent of class at most for any , then the group is nilpotent of -bounded class.
2. If and is nilpotent of class at most for any , then the derived group is nilpotent of -bounded class.
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.
We characterize all simple unitarizable representations of the braid group on complex vector spaces of dimension . In particular, we prove that if and denote the two generating twists of , then a simple representation (for ) is unitarizable if and only if the eigenvalues of are distinct, satisfy and 0$"> for , where the are functions of the eigenvalues, explicitly described in this paper.
Suppose is a complex Hilbert space and is a bounded operator. For each closed set let denote the corresponding spectral manifold. Let denote the set of all points with the property that for any open neighborhood of In this paper we show that if is dominating in some bounded open set, then has a nontrivial invariant subspace. As a corollary, every Hilbert space operator which is a quasiaffine transform of a subdecomposable operator with large spectrum has a nontrivial invariant subspace.
Let be a monic polynomial of degree , with complex coefficients, and let be its monic factor. We prove an asymptotically sharp inequality of the form , where denotes the sup norm on a compact set in the plane. The best constant in this inequality is found by potential theoretic methods. We also consider applications of the general result to the cases of a disk and a segment.
A Lie subalgebra of is said to be finitary if it consists of elements of finite rank. We show that, if acts irreducibly on , and if is infinite-dimensional, then every non-trivial ascendant Lie subalgebra of acts irreducibly on too. When , it follows that the locally solvable radical of such is trivial. In general, locally solvable finitary Lie algebras over fields of characteristic are hyperabelian.
Let be a deformation of a normal Gorenstein surface singularity over the complex number field . We assume that is a neighborhood of the origin of . Then we prove that admits a simultaneous log-canonical model if and only if an invariant of each fiber is constant.
This article presents sufficient conditions for the positive definiteness of radial functions , , in terms of the derivatives of . The criterion extends and unifies the previous analogues of Pólya's theorem and applies to arbitrarily smooth functions. In particular, it provides upper bounds on the Kuttner-Golubov function which gives the minimal value of such that the truncated power function , , is positive definite. Analogous problems and criteria of Pólya type for -dependent functions, 0$">, are also considered.
In this note we prove that for any two integers 1$"> there exist finite -groups of class such that and .
If is a surjective local homomorphism with kernel , such that and the conormal module has a free summand of rank , then the degree central subspace of the homotopy Lie algebra of has dimension greater than or equal to . This is a corollary of the Main Theorem of this note. The techniques involved provide new proofs of some well known results concerning the conormal module.
In this paper we prove that if is a cardinal in , then there is an inner model such that has no elementary end extension. In particular if exists, then weak compactness is never downwards absolute. We complement the result with a lemma stating that any cardinal greater than of uncountable cofinality in is Mahlo in every strict inner model of .
Let be a reflexive algebra in Banach space such that both and in Lat . Then every local derivation of into itself is a derivation.
Let be a convex and dominated statistical model on the measurable space , with minimal sufficient, and let . Then , the -algebra of all permutation invariant sets belonging to the -fold product -algebra , is shown to be minimal sufficient for the corresponding model for independent observations, .
The main technical tool provided and used is a functional analogue of a theorem of Grzegorek (1982) concerning generators of .
Let , , be the Kakeya maximal operator defined as the supremum of averages over tubes of the eccentricity . We shall prove the so-called Fefferman-Stein type inequality for ,
in the range , , with some constants and independent of and the weight .
Let be a field and . There exist a differential graded -module and various approximations to a differential on one of which gives a non-trivial deformation, another is obstructed, and another is unobstructed at order . The analogous problem in the category of -algebras in characteristic zero remains a long-standing open question.
We construct symmetric numerical semigroups for every minimal number of generators and multiplicity , . Furthermore we show that the set of their defining congruence is minimally generated by elements.