Journal of Operator Theory

Volume 37, Issue 1, Winter 1997 pp. 23-34.

Dense barreled spaces in Hardy spaces

Authors: Daniel Suárez
Author institution:Department of Mathematics, University of California, Berkeley, CA 94720, U.S.A. Current address: Instituto Argentino de Matemática, Viamonte 1636, 1er. Cuerpo, 1er. Piso, 1055 Buenos Aires, ARGENTINA

Summary: For $1 \le q \le \infty$ let $K^q$ be the set of all the noncyclic vectors for the backward shift operator acting on the Hardy space $H^q$. We show that a closed operator densely defined on $H^q$ with values in a Banach space is bounded if and only if its natural domain contains $K^q$.

Keywords: Backward shift, noncyclic vectors, Banach-Steinhaus manifold.

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