Order spectrum of the Cesàro operator in Banach lattice sequence spaces

SPECTRUM AND COMPACTNESS OF THE CESÀRO OPERATOR ON WEIGHTED ` p SPACES

An investigation is made of the continuity, the compactness and the spectrum of the Cesàro operator C when acting on the weighted Banach sequence spaces `p(w), 1 < p <∞, for a positive, decreasing weight w, thereby extending known results for C when acting on the classical spaces `p.

A New Class of Banach Sequence Spaces

Banach sequence spaces

Interpolation between Hilbert , Banach and Operator spaces

Motivated by a question of Vincent Lafforgue, we study the Banach spaces X satisfying the following property: there is a function ε → ∆ X (ε) tending to zero with ε > 0 such that every operator T : L 2 → L 2 with T ≤ ε that is simultaneously contractive (i.e. of norm ≤ 1) on L 1 and on L ∞ must be of norm ≤ ∆ X (ε) on L 2 (X). We show that ∆ X (ε) ∈ O(ε α) for some α > 0 iff X is isomorphic to ...

Operator Self-similar Processes on Banach Spaces

Operator self-similar (OSS) stochastic processes on arbitrary Banach spaces are considered. If the family of expectations of such a process is a spanning subset of the space, it is proved that the scaling family of operators of the process under consideration is a uniquely determinedmultiplicative group of operators. If the expectation-function of the process is continuous, it is proved that th...