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1. CMB Online first
On Closed Ideals in a Certain Class of Algebras of Holomorphic Functions We recently introduced a weighted Banach algebra $\mathfrak{A}_G^n$ of
functions which are holomorphic on the unit disc $\mathbb{D}$, continuous
up to the boundary and of the class $C^{(n)}$ at all points where
the function $G$ does not vanish. Here, $G$ refers to a function
of the disc algebra without zeros on $\mathbb{D}$. Then we proved that
all closed ideals in $\mathfrak{A}_G^n$ with at most countable hull are
standard. In the present paper, on the assumption that $G$ is
an outer function in $C^{(n)}(\overline{\mathbb{D}})$ having infinite roots
in $\mathfrak{A}_G^n$ and countable zero set $h(G)$, we show that all the
closed ideals $I$ with hull containing $h(G)$ are standard.
Keywords:Banach algebra, disc algebra, holomorphic spaces, standard ideal Categories:46J15, 46J20, 30H50 |
2. CMB 2011 (vol 54 pp. 338)
SzegÃ¶'s Theorem and Uniform Algebras We study SzegÃ¶'s theorem for a uniform algebra.
In particular, we do it for the disc algebra or the bidisc algebra.
Keywords:SzegÃ¶'s theorem, uniform algebras, disc algebra, weighted Bergman space Categories:32A35, 46J15, 60G25 |
3. CMB 2008 (vol 51 pp. 378)
Cyclic Vectors in Some Weighted $L^p$ Spaces of Entire Functions In this paper,
we generalize a result recently obtained by the author.
We characterize the cyclic vectors in $\Lp$.
Let $f\in\Lp$ and $f\poly$ be contained in the space.
We show that $f$ is non-vanishing if and only if $f$ is cyclic.
Keywords:weighted $L^p$ spaces of entire functions, cyclic vectors Categories:47A16, 46J15, 46H25 |