Related papers: $M$-ideals in $H^\infty(\mathbb{D})$

Let $X$ be a ball quasi-Banach function space, $\alpha\in \mathbb{R}$ and $q\in(0,\infty)$. In this paper, the authors first introduce the Herz-type Hardy space $\mathcal{H\dot{K}}_{X}^{\alpha,\,q}({\mathbb {R}}^n)$, which is defined via…

Properties of Lipschitz and d.c. surfaces of finite codimension in a Banach space, and properties of generated $\sigma$-ideals are studied. These $\sigma$-ideals naturally appear in the differentiation theory and in the abstract…

We analyze the singularities of rational inner functions on the unit bidisk and study both when these functions belong to Dirichlet-type spaces and when their partial derivatives belong to Hardy spaces. We characterize derivative…

Let $(\mathcal{X},d,\mu)$ be a doubling metric measure space in the sense of R. R. Coifman and G. Weiss, $L$ a non-negative self-adjoint operator on $L^2(\mathcal{X})$ satisfying the Davies--Gaffney estimate, and $X(\mathcal{X})$ a ball…

Let $X$ be a ball quasi-Banach function space satisfying some minor assumptions. In this article, the authors establish the characterizations of $H_X(\mathbb{R}^n)$, the Hardy space associated with $X$, via the Littlewood--Paley…

In this paper we study an algebraic and topological structure inside the following sets of special functions: Bloch functions defined on the open unit disk that are unbounded and analytic functions of bounded type defined a Banach algebra E…

The set of all maximal ideals of the ring $\mathcal{M}(X,\mathcal{A})$ of real valued measurable functions on a measurable space $(X,\mathcal{A})$ equipped with the hull-kernel topology is shown to be homeomorphic to the set $\hat{X}$ of…

Under certain hypotheses on the Banach space $X$, we prove that the set of analytic functions in $\mathcal{A}_u(X)$ (the algebra of all holomorphic and uniformly continuous functions in the ball of $X$) whose Aron-Berner extensions attain…

We determine the solid hull and solid core of weighted Banach spaces $H_v^\infty$ of analytic functions $f$ such that $v|f|$ is bounded, both in the case of the holomorphic functions on the disc and on the whole complex plane, for a very…

We study the maximal ideal space of $H^\infty(B)$, where $B$ is the unit ball of $\CC^n$. Following the lead of Gleason and Schark, we analyze Gleason parts, fibers, the S\u{\i}lov boundary, and other aspects of this Banach algebra. Our…

The main result is that there are infinitely many; in fact, a continuum; of closed ideals in the Banach algebra $L(L_1)$ of bounded linear operators on $L_1(0,1)$. This answers a question from A. Pietsch's 1978 book "Operator Ideals". The…

We consider pairs of Banach spaces (M_0, M) such that M_0 is defined in terms of a little-o condition, and M is defined by the corresponding big-O condition. The construction is general and pairs include function spaces of vanishing and…

For $\lambda\ge0$, the so-called $\lambda$-analytic functions are defined in terms of the (complex) Dunkl operators $D_{z}$ and $D_{\bar{z}}$. In the paper we introduce a Bloch type space on the disk ${\mathbb D}$ associated with…

Let $\mathscr{B}(X)$ denote the Banach algebra of bounded operators on $X$, where~$X$ is either Tsirelson's Banach space or the Schreier space of order $n$ for some $n\in\mathbb N$. We show that the lattice of closed ideals…

A concept of boundedness of the $\mathbf{L}$-index in joint variables (see in Bandura A. I., Bordulyak M. T., Skaskiv O. B. "Sufficient conditions of boundedness of L-index in joint variables", Mat. Stud. 45 (2016), 12--26.…

The theory of M-ideals and multiplier mappings of Banach spaces naturally generalizes to left (or right) M-ideals and multiplier mappings of operator spaces. These subspaces and mappings are intrinsically characterized in terms of the…

We study $C$-rich spaces, lush spaces, and $C$-extremely regular spaces concerning with the Mazur-Ulam property. We show that a uniform algebra and the real part of a uniform algebra with the supremum norm are $C$-rich spaces, hence lush…

The algebra $H^\infty(D)$ of bounded holomorphic functions on $D\subset\mathbb C$ is projective free for a wide class of infinitely connected domains. In particular, for such $D$ every rectangular left-invertible matrix with entries in…

Given a von Neumann algebra $M$ and a $W^{\ast}$-correspondence $E$ over $M$, we construct an algebra $H^{\infty}(E)$ that we call the Hardy algebra of $E$. When $M=\mathbb{C}=E$, then $H^{\infty}(E)$ is the classical Hardy space…

The paper is concerned with defining a topology on the set of ideals of codimension d of the algebra C^\infty(M,R) with M being a compact smooth manifold. Its main property is that it is compact Hausdorff and it contains as a subspace the…