M. J. Crabb

Some inequalities for norm unitaries in Banach algebras

Let A be a complex unital Banach algebra. An element u ∈ A is a norm unitary if (For the algebra of all bounded operators on a Banach space, the norm unitaries arethe invertible isometries.) Given a norm unitary u ∈ A , we have Sp( u )⊃Γ, where Sp( u ) denotes the spectrum of u and Γ denotes the unit circle in C . If Sp( u )≠Γ we may suppose, by replacing e iθ u , that . Then there exists h ∈ A such that

On one-sided primitivity of Banach algebras

Let

Polynomials in a hermitian element

S

Some extremal algebras for hermitians

be the semigroup with identity, generated by

THE EXTREMAL ALGEBRA ON TWO HERMITIANS WITH SQUARE 1

x

Interpolation and inequalities for functions of exponential type: the Arens irregularity of an extremal algebra

and

Characterizations of commutativity for C *-algebras

y

Hermitian powers: A Muntz theorem and extremal algebras

, subject to

The primitivity of semigroup algebras of free products

y

Finiteness and recognizability problems for substitution maps on two symbols

being invertible and