A remark on contracting inverse semigroups

Primer on Inverse Semigroups

A Remark on Hypercontractive Semigroups and Operator Ideals

In this note, we answer a question raised by Johnson and Schechtman [7], about the hypercontractive semigroup on {−1, 1}. More generally, we prove the theorem below. 2000 Math. Subject Classification: Primary 47D20. Seconday 47L20. In this note, we answer a question raised by Johnson and Schechtman [7]. We refer to their paper for motivation and background. In addition, we refer the reader to [...

A remark of contraction semigroups on Banach spaces

Let X be a complex Banach space and let J : X → X∗ be a duality section on X (i.e. 〈x, J(x)〉 = ‖J(x)‖‖x‖ = ‖J(x)‖2 = ‖x‖2). For any unit vector x and any (C0) contraction semigroup T = {e tA : t ≥ 0}, Goldstein proved that if X is a Hilbert space and if |〈T (t)x, J(x)〉| → 1 as t → ∞, then x is an eigenvector of A corresponding to a purely imaginary eigenvalue. In this article, we prove the simi...

Inverse Semigroups Acting on Graphs

There has been much work done recently on the action of semigroups on sets with some important applications to, for example, the theory and structure of semigroup amalgams. It seems natural to consider the actions of semigroups on sets ‘with structure’ and in particular on graphs and trees. The theory of group actions has proved a powerful tool in combinatorial group theory and it is reasonable...

A Note on Amalgams of Inverse Semigroups