Ferenc Lukács type theorems in terms of the Abel-Poisson mean of conjugate series

A theorem of Ferenc Lukács determines the generalized jumps of a periodic, Lebesgue integrable function in terms of the partial sum of the conjugate series to the Fourier series of . The main aim of this paper is to prove an analogous theorem in terms of the Abel-Poisson mean. We also prove an estimate of the partial derivative (with respect to the angle) of the Abel-Poisson mean of an integrable function at those points at which is smooth. Finally, we reveal the intimate relation between these two results.

     

Locally pre-*-equivalent algebras

We prove a weaker form of Cuntz's theorem: every locally pre--equivalent Banach *-algebra is -equivalent. Using this result, we obtain local conditions for the existence of an equivalent -norm.

     

Hilbertian Versus Hilbert W*-Modules and Applications to L2- and other invariants

Hilbert(ian) A-modules over finite von Neumann algebras with a faithful normal trace state (from global analysis) and Hilbert W*-modules over A (from operator algebra theory) are compared and a categorical equivalence is established. The correspondence between these two structures sheds new light on basic results in L ²-invariant theory providing alternative proofs. We indicate new invariants for finitely generated projective B-modules, where B is a unital C*-algebra (usually the full group C*-algebra C*() of the fundamental group =₁(M) of a manifold M).     

On subnormal operators

LetS be a pure subnormal operator such thatC*(S), theC*-algebra generated byS, is generated by a unilateral shiftU of multiplicity 1. We obtain conditions under which 5 is unitarily equivalent toα + βU, α andβ being scalars orS hasC*-spectral inclusion property. It is also proved that if in addition,S hasC*-spectral inclusion property, then so does its dualT andC*(T) is generated by a unilateral shift of multiplicity 1. Finally, a characterization of quasinormal operators among pure subnormal operators is obtained.     

有界广义逆模映射的刻画及其应用

本文引入了有界广义逆模映射的概念,并给出了等价刻画．然后利用它为工具获得了一类重要的有界模映射的因子分解定理,使得著名的Douglas分解定理成为其特例．     

Free C-Algebras and the Problem of Uniquenes of Extension in Non-commutative Hahn-Banach Theorem

ＦｒｅＣ＊┐ＡｌｇｅｂｒａｓａｎｄｔｈｅＰｒｏｂｌｅｍｏｆＵｎｉｑｕｅｎｅｓｏｆＥｘｔｅｎｓｉｏｎｉｎＮｏｎ┐ｃｏｍｍｕｔａｔｉｖｅＨａｈｎ┐ＢａｎａｃｈＴｈｅｏｒｅｍ＊）ＺｈａｎｇＬｕｎｃｈｕａｎ（张伦传）ａｎｄＭａＪｉｐｕ（马吉溥）（Ｄｅｐａｒｔ...     

交换的实W~*-代数

本文指出，交换的（复）Ｗ 代数的大部分结果对于实情形仍然成立，自然有周期为２同胚的差别．此外，不同于复情形，可分实Ｈｉｌｂｅｒｔ空间中不包含任何极小投影的交换实ＶＮ代数同构于Ｌ∞（［０，１］），Ｌ∞ｒ（［０，１］）或Ｌ∞（［０，１］）Ｌ∞ｒ（［０，１］）．     

Derivations implemented by local multipliers

A condition on a derivation of an arbitrary C*-algebra is presented entailing that it is implemented as an inner derivation by a local multiplier.

     

A boolean transfer principle from L*-Algebras to AL*-Algebras

Just as Kaplansky [4] has introduced the notion of an AW*-module as a generalization of a complex Hilbert space, we introduce the notion of an AL*-algebra, which is a generalization of that of an L*-algebra invented by Schue [9, 10]. By using Boolean valued methods developed by Ozawa [6–8], Takeuti [11–13] and others, we establish its basic properties including a fundamental structure theorem. This paper should be regarded as a continuation or our previous paper [5], the familiarity with which is presupposed. MSC: 03C90, 03E40, 17B65, 46L10.