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Joshua Isralowitz

Publications and source records attributed to Joshua Isralowitz.

23 records · Page 2Linked to original sources
arXiv2014

Compactness and essential norm properties of operators on generalized Fock spaces

The purpose of this paper is to systematically study compactness and essential norm properties of operators on a very general class of weighted Fock spaces over $\C$. In particular, we obtain rather strong necessary and sufficient conditions for a wide class of operators (which includes operators in the Toeplitz algebra generated by bounded symbols) to be compact and we obtain related estimates on the essential norm of such operators. Finally, we discuss interesting open problems related to our results, and in particular discuss the possibility of extending our results to other generally weighted Bergman spaces on the unit ball of $\C$.

math.FA↗
arXiv2014

Invertible Toeplitz products, weighted norm inequalities, and A${}_p$ weights

In this paper, we characterize invertible Toeplitz products on a number of Banach spaces of analytic functions, including weighted Bergman space $L^p_a (\mathbb{B}_n, dv_γ)$, the Hardy space $H^p(\partial \mathbb{D})$, and the weighted Fock space F${}_α^p$ for $p > 1$. The common tool in the proofs of our characterizations will be the theory of weighted norm inequalities and A${}_p$ type weights. Moreover, we analyze and compare the various A${}_p$ type conditions that arise in our characterizations. Finally, we extend the "reverse Hölder inequality" of Zheng and Stroethoff \cite{SZ1, SZ2} for $p = 2$ to the general case of $p > 1$.

math.CA↗
arXiv2013

Compactness of operators on generalized Fock spaces

For a very general class of weighted Fock spaces on $\mathbb{C}^n$, we give necessary and sufficient conditions for a Toeplitz operator with a (not necessarily positive) measure symbol to be compact. Furthermore, we show that all compact operators are in the norm closure of the algebra generated by Toeplitz operators with $C_c ^\infty(\mathbb{C}^n)$ symbols, and in the Hilbert space setting show that all compact operators are in the norm closure of the set of such Toeplitz operators.

math.FA↗
arXiv2012

Schatten $p$ class commutators on the weighted Bergman space $L^2_a (\mathbb{B}_n, dv_γ)$ for $\frac{2n}{n + 1 + γ} < p < \infty$

Let $P_γ$ be the orthogonal projection from the space $L ^2 (\mathbb{B}_n, dv_γ)$ to the standard weighted Bergman space $L_a ^2 (\mathbb{B}_n, dv_γ)$. In this paper, we characterize the Schatten $p$ class membership of the commutator $[M_f, P_γ]$ when $\frac{2n}{n + 1 + γ} < p < \infty$. In particular, if $\frac{2n}{n + 1 + γ} < p < \infty$, then we show that $[M_f, P_γ]$ is in the Schatten $p$ class if and only if the mean oscillation MO${}_γ(f)$ is in $ L^p(\mathbb{B}_n, dζ)$ where $dζ$ is the Möbius invariant measure on $\mathbb{B}_n.$ This answers a question recently raised by K. Zhu.

math.FA↗