Geometry of operator spaces.

Quasimultipliers of Operator Spaces

We use the injective envelope to study quasimultipliers of operator spaces. We prove that all representable operator algebra products that an operator space can be endowed with are induced by quasimultipliers. We obtain generalizations of the Banach-Stone theorem.

The Libera operator on Dirichlet spaces

In this paper, we consider the boundedness of the Libera operator on Dirichlet spaces in terms of the Schur test. Moreover, we get its point spectrum and norm.

Operator-valued bases on Hilbert spaces

In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...

What are operator spaces ? Operator algebra group

Geometry of Twistor Spaces

To motivate the construction, let us begin by looking at the much simpler situation that arises in real dimension 2. First of all, we all know that a complex curve (or Riemann surface) is the same thing as an oriented 2manifoldM equipped with a conformal class [g] of Riemannian (i.e. positivedefinite) metrics. If g is any Riemannian metric on M , and if u : M → R is any smooth positive function...