闭极大三角代数的对角不交理想

研究了闭极大三角代数的对角不交理想中有限秩算子的性质,并利用这些性质讨论了几种特殊的对角不交理想     

Non-singly-generated closed ideals in group algebras

We investigate the problem whether every closed ideal in the group algebrasA(G) is generated by a single function. For the algebrasA _r(R ⁿ),n≧6, we give a negative solution. We also obtain some negative results for general locally compact abelian groups. This paper is a part of the author’s Ph. D. thesis prepared at the Hebrew University of Jerusalem under the supervision of Professor Y. Katznelson, to whom the author wishes to express his thanks for his helpful guidance, and valuable remarks.     

Relatively regular ideals in semiprime Banach algebras

Nella prima parte di questo lavoro vengono studiate le relazioni che intercorrono tra il concetto di relativa regolarità in un'algebra non necessariamente unitaria ed alcuni ideali (radicale, zoccolo, prezoccolo) che intervengono nello sviluppo della teoria di Fredholm in algebre di Banach. Nella seconda parte del lavoro viene dimostrato che in certe algebre di BanachA complesse semiprime l'esistenza di un ideale relativamente regolare chiuso implica cheA è unitaria e di dimensione finita.     

On identifying the maximal ideals in Banach algebras

We consider the problem of identifying the maximal ideals of a Banach algebra S that is contained in a larger Banach algebra B. If S is dense in B in an appropriate sense and if the spectral radii in S and B are the same, then S and B have the same maximal ideals. The result is illustrated by two examples of Banach algebras S in which the density and spectral radius conditions are easily shown to be valid with respect to a larger algebra B whose maximal ideals are known. The first example is a convolution algebra on a group where the functions in the algebra have specified rate of decay. The second example is a generalized version of an algebra introduced by I. Hirschman. Two applications of the generalized Hirschman algebra are presented: these relate to filtering and prediction of stationary random sequences and concern the asymptotic behavior of the errors incurred by the finite memory predictor and by the finite lag filter.     

Topological properties of regular generalized function algebras

We investigate the topological density of various subalgebras of regular generalized functions in the Colombeau algebra $\mathcal{G }(\varOmega )$ of generalized functions with its natural (so-called sharp) topology.     

Non-closed sums of closed ideals in Banach algebras

A major difficulty in Banach algebra theory is that sums of closed ideals need not be closed. We survey the known results and present examples showing that they are in most directions the best possible. We also give a new sufficient condition for closure in the uniform algebra setting.

     

On maximal ideals of codimension one in m-convex algebras

In Studia Math. 58:291–298, 1976, W. Żelazko gives a characterization of complex commutative complete unital m-convex algebras in which all maximal ideals are of codimension one. In these algebras every element has a bounded spectrum.

Here we present a similar result concerning sufficient conditions so that all maximal ideals of a complex commutative unital m-convex algebra to be of codimension one. Moreover, these conditions are proved to be equivalent to each other. We also give an example of a complex commutative unital advertibly complete m-convex algebra such that all its maximal ideals are of codimension one and has an element with unbounded spectrum.

     

Weakly closed Jordan ideals in nest algebras on Banach spaces

We show that weakly closed Jordan ideals in nest algebras on Banach spaces are associative ideals. The decomposability of finite-rank operators in Jordan ideals and the commutants of bimodules are also investigated. Author’s address: J. Li and F. Lu, Department of Mathematics, Suzhou University, Suzhou 215006, People’s Republic of China This research was supported by NNSFC (No. 10771154) and PNSFJ (NO. BK2007049).     

Weakly closed Jordan ideals in nest algebras on Banach spaces

We show that weakly closed Jordan ideals in nest algebras on Banach spaces are associative ideals. The decomposability of finite-rank operators in Jordan ideals and the commutants of bimodules are also investigated.     

On maximal ideals in two algebras of operator valued analytic functions

The maximal ideals in two algebras of operator valued analytic functions in the unit disc are described.     

Finite rank operators in closed maximal triangular algebras II

In this paper, we discuss finite rank operators in a closed maximal triangular algebra . Based on the following result that each finite rank operator of can be written as a finite sum of rank one operators each belonging to , we proved that , where , if ; and , if . We also proved that the Erdos Density Theorem holds in if and only if is strongly reducible.

     

On abelian subalgebras and ideals of maximal dimension in supersolvable Lie algebras

In this paper, the main objective is to compare the abelian subalgebras and ideals of maximal dimension for finite-dimensional supersolvable Lie algebras. We characterise the maximal abelian subalgebras of solvable Lie algebras and study solvable Lie algebras containing an abelian subalgebra of codimension 2. Finally, we prove that nilpotent Lie algebras with an abelian subalgebra of codimension 3 contain an abelian ideal with the same dimension, provided that the characteristic of the underlying field is not 2. Throughout the paper, we also give several examples to clarify some results.     

Topological and bornological characterisations of ideals in von Neumann algebras: I

Suppose is a von Neumann algebra on a Hilbert space and is any ideal in . We determine a topology on , for which the members of that are to norm continuous are exactly those in ; and a bornology on such that the elements of which map the unit ball to an element of , equivalently those members of that are norm to bounded, are exactly those in . This is achieved via analogues of the notions of injectivity and surjectivity in the theory of operator ideals on Banach spaces.