Balanced metrics on Cartan and Cartan-Hartogs domains

This paper consists of two results dealing with balanced metrics (in S. Donaldson terminology) on nonconpact complex manifolds. In the first one we describe all balanced metrics on Cartan domains. In the second one we show that the only Cartan-Hartogs domain which admits a balanced metric is the complex hyperbolic space. By combining these results with those obtained in [13] (Kaehler-Einstein submanifolds of the infinite dimensional projective space, to appear in Mathematische Annalen) we also provide the first example of complete, Kaehler-Einstein and projectively induced metric g such that $\alpha g$ is not balanced for all $\alpha >0$.Comment: 11 page

Weakly coupled bound states of Pauli operators

We consider the two-dimensional Pauli operator perturbed by a weakly coupled, attractive potential. We show that besides the eigenvalues arising from the Aharonov-Casher zero modes there are two or one (depending on whether the flux of the magnetic field is integer or not) additional eigenvalues for arbitrarily small coupling and we calculate their asymptotics in the weak coupling limit.Comment: 19 page

Wigner transform and pseudodifferential operators on symmetric spaces of non-compact type

We obtain a general expression for a Wigner transform (Wigner function) on symmetric spaces of non-compact type and study the Weyl calculus of pseudodifferential operators on them

Noncommutative Figa-Talamanca-Herz algebras for Schur multipliers

We introduce a noncommutative analogue of the Fig\'a-Talamanca-Herz algebra $A_p(G)$ on the natural predual of the operator space $\frak{M}_{p,cb}$ of completely bounded Schur multipliers on Schatten space $S_p$. We determine the isometric Schur multipliers and prove that the space $\frak{M}_{p}$ of bounded Schur multipliers on Schatten space $S_p$ is the closure in the weak operator topology of the span of isometric multipliers.Comment: 24 pages; corrected typo

Applications of Hilbert Module Approach to Multivariable Operator Theory

A commuting $n$-tuple $(T_1, \ldots, T_n)$ of bounded linear operators on a Hilbert space \clh associate a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z_1, \ldots, z_n]$ in the following sense: $$\mathbb{C}[z_1, \ldots, z_n] \times \mathcal{H} \rightarrow \mathcal{H}, \quad \quad (p, h) \mapsto p(T_1, \ldots, T_n)h,$$where $p \in \mathbb{C}[z_1, \ldots, z_n]$ and $h \in \mathcal{H}$. A companion survey provides an introduction to the theory of Hilbert modules and some (Hilbert) module point of view to multivariable operator theory. The purpose of this survey is to emphasize algebraic and geometric aspects of Hilbert module approach to operator theory and to survey several applications of the theory of Hilbert modules in multivariable operator theory. The topics which are studied include: generalized canonical models and Cowen-Douglas class, dilations and factorization of reproducing kernel Hilbert spaces, a class of simple submodules and quotient modules of the Hardy modules over polydisc, commutant lifting theorem, similarity and free Hilbert modules, left invertible multipliers, inner resolutions, essentially normal Hilbert modules, localizations of free resolutions and rigidity phenomenon. This article is a companion paper to "An Introduction to Hilbert Module Approach to Multivariable Operator Theory".Comment: 46 pages. This is a companion paper to arXiv:1308.6103. To appear in Handbook of Operator Theory, Springe

Isoperimetric inequalities for some integral operators arising in potential theory

In this paper we review our previous isoperimetric results for the logarithmic potential and Newton potential operators. The main reason why the results are useful, beyond the intrinsic interest of geometric extremum problems, is that they produce a priori bounds for spectral invariants of operators on arbitrary domains. We demonstrate these in explicit examples.Comment: This conference paper gives a review of our previous results in the subjec

Operator theory and function theory in Drury-Arveson space and its quotients

The Drury-Arveson space $H^2_d$, also known as symmetric Fock space or the $d$-shift space, is a Hilbert function space that has a natural $d$-tuple of operators acting on it, which gives it the structure of a Hilbert module. This survey aims to introduce the Drury-Arveson space, to give a panoramic view of the main operator theoretic and function theoretic aspects of this space, and to describe the universal role that it plays in multivariable operator theory and in Pick interpolation theory.Comment: Final version (to appear in Handbook of Operator Theory); 42 page

Duality and distance formulas in spaces defined by means of oscillation

For the classical space of functions with bounded mean oscillation, it is well known that VMO∗∗=BMOVMO∗∗=BMO and there are many characterizations of the distance from a function f in BMOBMO to VMOVMO. When considering the Bloch space, results in the same vein are available with respect to the little Bloch space. In this paper such duality results and distance formulas are obtained by pure functional analysis. Applications include general Möbius invariant spaces such as QK-spaces, weighted spaces, Lipschitz–Hölder spaces and rectangular BMOBMO of several variables

Effect of prior treatments on selinexor, bortezomib, and dexamethasone in previously treated multiple myeloma

Therapeutic regimens for previously treated multiple myeloma (MM) may not provide prolonged disease control and are often complicated by significant adverse events, including peripheral neuropathy. In patients with previously treated MM in the Phase 3 BOSTON study, once weekly selinexor, once weekly bortezomib, and 40 mg dexamethasone (XVd) demonstrated a significantly longer median progression-free survival (PFS), higher response rates, deeper responses, a trend to improved survival, and reduced incidence and severity of bortezomib-induced peripheral neuropathy when compared with standard twice weekly bortezomib and 80 mg dexamethasone (Vd). The pre-specified analyses described here evaluated the influence of the number of prior lines of therapy, prior treatment with lenalidomide, prior proteasome inhibitor (PI) therapy, prior immunomodulatory drug therapy, and prior autologous stem cell transplant (ASCT) on the efficacy and safety of XVd compared with Vd. In this 1:1 randomized study, enrolled patients were assigned to receive once weekly oral selinexor (100 mg) with once weekly subcutaneous bortezomib (1.3 mg/m2) and 40 mg per week dexamethasone (XVd) versus standard twice weekly bortezomib and 80 mg per week dexamethasone (Vd). XVd significantly improved PFS, overall response rate, time-to-next-treatment, and showed reduced all grade and grade ≥ 2 peripheral neuropathy compared with Vd regardless of prior treatments, but the benefits of XVd over Vd were more pronounced in patients treated earlier in their disease course who had either received only one prior therapy, had never been treated with a PI, or had prior ASCT. Treatment with XVd improved outcomes as compared to Vd regardless of prior therapies as well as manageable and generally reversible adverse events. XVd was associated with clinical benefit and reduced peripheral neuropathy compared to standard Vd in previously treated MM. These results suggest that the once weekly XVd regimen may be optimally administered to patients earlier in their course of disease, as their first bortezomib-containing regimen, and in those relapsing after ASCT. Trial registration: ClinicalTrials.gov (NCT03110562). Registered 12 April 2017. https://clinicaltrials.gov/ct2/show/NCT03110562

Once-weekly selinexor, bortezomib, and dexamethasone versus twice-weekly bortezomib and dexamethasone in patients with multiple myeloma (BOSTON): a randomised, open-label phase 3 trial

Background Selinexor with dexamethasone has demonstrated activity in patients with heavily pretreated multiple myeloma (MM). In a phase 1b/2 study, the combination of oral selinexor with the proteasome inhibitor (PI) bortezomib, and dexamethasone (SVd) induced high response rates with low rates of peripheral neuropathy, the main dose-limiting toxicity of bortezomib. The aim of this trial was to evaluate the clinical benefit of weekly SVd versus standard bortezomib and dexamethasone (Vd) in patients with previously treated MM. Methods This phase 3, randomised, open label trial was conducted at 123 sites in 21 countries. Patients who were previously treated with one to three lines of therapy, including PIs were randomised (1:1) to selinexor (100 mg once-weekly) plus bortezomib (1·3 mg/m2 once-weekly) and dexamethasone (20 mg twice-weekly) [SVd] or bortezomib (1·3 mg/m2 twice-weekly) and dexamethasone (20 mg 4 times per week) [Vd]. Randomisation was done using interactive response technology and stratified by previous PI therapy, lines of treatment, and MM stage. The primary endpoint was progression-free survival (PFS) in the intention-to-treat population. Patients who received at least one dose of study treatment were included in the safety population. This trial is registered at ClinicalTrials.gov, NCT03110562. Findings Between June 2017 and February 2019, 402 patients were randomised: 195 to SVd and 207 to Vd. Median PFS was 13·93 (95% CI 11·73–NE) with SVd versus 9·46 months (8·11–10·78) with Vd; HR 0·70, [95% CI 0·53–0·93]; P=0.0075. Most frequent grade ≥3 adverse events (SVd vs Vd) were thrombocytopenia (77 [40%] vs 35 [17%]), fatigue (26 [13%] vs 2 [1%]), anaemia (31 [16%] vs 20 [10%]), and pneumonia (22 [11%] vs 22 [11%]). Peripheral neuropathy rates (overall, 32·3% vs 47·1%; OR 0·52, [95% CI 0·35-0·79]; P=0.0010 and grade ≥2, 21·0% vs 34·3%; OR 0·50, [95% CI 0·32-0·79]; P=0.0013) were lower with SVd. There were 47 (24%) deaths on SVd and 62 (30%) on Vd. Interpretation Once-weekly SVd is a novel, effective, and convenient treatment option for patients with MM who have received 1-3 prior therapies. Funding Karyopharm Therapeutics In