On local ergodic theorems for positive semigroups
A multiplicative semigroup of idempotent operators is called an operator band. We prove that for each K>1 there exists an irreducible operator band on the Hilbert space which is norm-bounded by K. This implies that there exists an irreducible operator band on a Banach space such that each member has operator norm equal to 1. Given a positive integer r, we introduce a notion of weak r-transitivity of a set of bounded operators on a Banach space. We construct an operator band on that is weakly...
A two-sided sequence with values in a complex unital Banach algebra is a cosine sequence if it satisfies for any n,m ∈ ℤ with c₀ equal to the unity of the algebra. A cosine sequence is bounded if . A (bounded) group decomposition for a cosine sequence is a representation of c as for every n ∈ ℤ, where b is an invertible element of the algebra (satisfying , respectively). It is known that every bounded cosine sequence possesses a universally defined group decomposition, the so-called...
Si studiano esistenza, unicità e regolarità delle soluzioni strette, classiche e forti dell'equazione di evoluzione non autonoma con il dato iniziale , in uno spazio di Banach . Gli operatori sono generatori infinitesimali di semi-gruppi analitici ed hanno dominio indipendente da e non necessariamente denso in . Si danno condizioni necessarie e sufficienti per l'esistenza e la regolarità hölderiana della soluzione e della sua derivata.