Homomorphic Retractions in Semigroups

Homomorphic Retractions in Semigroups

Homomorphic Conditional Expectations as Noncommutative Retractions

Let A be a C∗-algebra and E : A → A a conditional expectation. The Kadison-Schwarz inequality for completely positive maps, E(x)∗E(x) ≤ E(x∗x), implies that ‖E(x)‖ ≤ ‖E(x∗x)‖ . In this note we show that E is homomorphic (in the sense that E(xy) = E(x)E(y) for every x, y in A) if and only if ‖E(x)‖ = ‖E(x∗x)‖ , for every x in A. We also prove that a homomorphic conditional expectation on a commu...

Retractions in Intersection Types

This paper deals with retraction intended as isomorphic embedding in intersection types building left and right inverses as terms of a λ-calculus with a ⊥ constant. The main result is a necessary and sufficient condition two strict intersection types must satisfy in order to assure the existence of two terms showing the first type to be a retract of the second one. Moreover, the characterisatio...

Retractions in orthopaedic research

OBJECTIVES Despite the fact that research fraud and misconduct are under scrutiny in the field of orthopaedic research, little systematic work has been done to uncover and characterise the underlying reasons for academic retractions in this field. The purpose of this study was to determine the rate of retractions and identify the reasons for retracted publications in the orthopaedic literature....

Projections and Retractions

The main result of this paper is a generalization of a theorem of R. S. Phillips [6] on the nonexistence of projections of l°° onto c0. If S is a locally compact Hausdorff space then let C(S) denote the space of bounded continuous real (or complex) valued functions on 5; also, let Co(S) be those functions in C(S) which vanish at infinity. If N is the space of positive integers with the discrete...