20 research outputs found
Semi-simplicity of a proper weak H
A weak right H*-algebra is a Banach algebra A which is a Hilbert space and which has a dense subset Dr with the property that for each x in Dr there exists xr such that (yx,z)=(y,zxr) for all y, z in A. It is shown that a proper (each xr is unique) weak right H*-algebra is semi-simple. Also there is an example of weak right H*-algebra which is not a left H*-algebra
Banach algebras with commuting idempotents, no identity
In a recent paper we showed that certain algebras, with identity, can be represented as algebras of continuous functions on a Boolean space (a totally disconnected compact space). Now we shall show that the same is essentially true even if we do not assume existence of an identity
An exotic characterization of a commutative H
Commutative H*-algebra is characterized in terms of the
property that the orthogonal complement of a right ideal is a left
ideal
Commuting idempotents of an H∗-algebra
Commutative H∗-algebra is characterized in terms of
idempotents. Here we offer three characterizations
Another version of “exotic characterization of a commutative H∗-algebra”
Commutative H∗-algebra is characterized in a somewhat unusual fashion without assuming either Hilbert space structure or commutativity. Existence of an involution is not postulated also
Banach algebras with commuting idempotents, no identity
In a recent paper we showed that certain algebras, with identity, can be represented as algebras of continuous functions on a Boolean space (a totally disconnected compact space). Now we shall show that the same is essentially true even if we do not assume existence of an identity
A simple characterization of the trace-class of operators
The trace-class (τc) of operators on a Hilbert space is characterized in terms of existence of certain centralizers
Totally disconnected compactifications
There is a one-to-one order preserving correspondence between totally disconnected
compactifications of a topological space and certain Boolean algebras of open closed subsets on
it