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