The Cesàro operator is bounded on $H\sp 1$
نویسندگان
چکیده
منابع مشابه
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.
متن کاملOn generalized absolute Cesàro summability
In this paper, a main theorem dealing with | C, 1 |k summability factors has been generalized under more weaker conditions for | C,α, β |k summability factors. This theorem also includes some new results. Mathematics Subject Classification 2000: 40D15, 40F05, 40G05, 40G99.
متن کاملA Polynomially Bounded Operator on Hilbert Space Which Is Not Similar to a Contraction
Let ε > 0. We prove that there exists an operator Tε : `2 → `2such that for any polynomial P we have ‖P (Tε)‖ ≤ (1 +ε)‖P‖∞, but Tε isnot similar to a contraction, i.e. there does not exist an invertible operatorS : `2 → `2 such that‖S−1TεS‖ ≤ 1. This answers negatively a question at-tributed to Halmos after his well-known 1970 paper (“Ten problems in Hilbertspace”). ...
متن کاملA Smoothing Operator for Boolean Operations on Surfel-Bounded Solids
We present a simple smoothing operator for surfel-bounded solids obtained by adding two solids together using boolean operations. When adding two surfel-bounded solids together with the union operator, it is sometimes desirable to smooth out the sharp creases in the surface of the resulting solid. This report presents a simple local smoothing operator for this purpose. We illustrate that this o...
متن کاملDivergence operator and Poincaré inequalities on arbitrary bounded domains
Let Ω be an arbitrary bounded domain of Rn. We study the right invertibility of the divergence on Ω in weighted Lebesgue and Sobolev spaces on Ω, and relate this invertibility to a geometric characterization of Ω and to weighted Poincaré inequalities on Ω. We recover, in particular, well-known results on the right invertibility of the divergence in Sobolev spaces when Ω is Lipschitz or, more ge...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1990
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1990-1021904-9