# Journal of Operator Theory

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

Dense barreled spaces in Hardy spaces**Authors**: Daniel Suarez

**Author institution:**Department of Mathematics, University of California, Berkeley, CA 94720, U.S.A. Current address: Instituto Argentino de MatemÃ¡tica, 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.

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