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On operator bands

Roman Drnovšek, Leo Livshits, Gordon MacDonald, Ben Mathes, Heydar Radjavi, Peter Šemrl (2000)

Studia Mathematica

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 l 2 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 l 2 that is weakly...

On operator-valued cosine sequences on UMD spaces

Wojciech Chojnacki (2010)

Studia Mathematica

A two-sided sequence ( c ) n with values in a complex unital Banach algebra is a cosine sequence if it satisfies c n + m + c n - m = 2 c c for any n,m ∈ ℤ with c₀ equal to the unity of the algebra. A cosine sequence ( c ) n is bounded if s u p n | | c | | < . A (bounded) group decomposition for a cosine sequence c = ( c ) n is a representation of c as c = ( b + b - n ) / 2 for every n ∈ ℤ, where b is an invertible element of the algebra (satisfying s u p n | | b | | < , respectively). It is known that every bounded cosine sequence possesses a universally defined group decomposition, the so-called...

On the abstract Cauchy problem in the case of constant domains

Paolo Acquistapace, Brunello Terreni (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si studiano esistenza, unicità e regolarità delle soluzioni strette, classiche e forti u 𝐂 ( [ 0 , T ] , E ) dell'equazione di evoluzione non autonoma u ( t ) - A ( t ) u ( t ) = f ( t ) con il dato iniziale u ( 0 ) = x , in uno spazio di Banach E . Gli operatori A ( t ) sono generatori infinitesimali di semi-gruppi analitici ed hanno dominio indipendente da t e non necessariamente denso in E . Si danno condizioni necessarie e sufficienti per l'esistenza e la regolarità hölderiana della soluzione e della sua derivata.

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