ترغب بنشر مسار تعليمي؟ اضغط هنا

The condenser quasicentral modulus

155   0   0.0 ( 0 )
 نشر من قبل Dan-Virgil Voiculescu
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We introduced the quasicentral modulus to study normed ideal perturbations of operators. It is a limit of condenser quasicentral moduli in view of a recently noticed analogy with capacity in nonlinear potential theory. We prove here some basic properties of the condenser quasicentral modulus and compute a simple example. Some of the results are in the more general setting of a semifinite von Neumann algebra.

قيم البحث

اقرأ أيضاً

A Banach space X has the SHAI (surjective homomorphisms are injective) property provided that for every Banach space Y, every continuous surjective algebra homomorphism from the bounded linear operators on X onto the bounded linear operators on Y is injective. The main result gives a sufficient condition for X to have the SHAI property. The condition is satisfied for L^p (0, 1) for 1 < p < infty, spaces with symmetric bases that have finite cotype, and the Schatten p-spaces for 1 < p < infty.
270 - L. Golinskii , V. Kadets 2020
In 2000 V. Lomonosov suggested a counterexample to the complex version of the Bishop-Phelps theorem on modulus support functionals. We discuss the $c_0$-analog of that example and demonstrate that the set of sup-attaining functionals is non-trivial, thus answering an open question, asked in cite{KLMW}.
88 - Enrico Boasso 2016
Given two complex Banach spaces $X_1$ and $X_2$, a tensor product $X_1tilde{otimes} X_2$ of $X_1$ and $X_2$ in the sense of [14], two complex solvable finite dimensional Lie algebras $L_1$ and $L_2$, and two representations $rho_icolon L_ito {rm L}(X _i)$ of the algebras, $i=1$, $2$, we consider the Lie algebra $L=L_1times L_2$, and the tensor product representation of $L$, $rhocolon Lto {rm L}(X_1tilde{otimes}X_2)$, $rho=rho_1otimes I +Iotimes rho_2$. In this work we study the S{l}odkowski and the split joint spectra of the representation $rho$, and we describe them in terms of the corresponding joint spectra of $rho_1$ and $rho_2$. Moreover, we study the essential S{l}odkowski and the essential split joint spectra of the representation $rho$, and we describe them by means of the corresponding joint spectra and the corresponding essential joint spectra of $rho_1$ and $rho_2$. In addition, with similar arguments we describe all the above-mentioned joint spectra for the multiplication representation in an operator ideal between Banach spaces in the sense of [14]. Finally, we consider nilpotent systems of operators, in particular commutative, and we apply our descriptions to them.
In this paper, we show that under a mild condition, a principal submodule of the Bergman module on a bounded strongly pseudoconvex domain with smooth boundary in $mathbb{C}^n$ is $p$-essentially normal for all $p>n$. This is a significant improvement of the results of the first author and K. Wang, where the same result is shown to hold for polynomial-generated principal submodules of the Bergman module on the unit ball $mathbb{B}_n$ of $mathbb{C}^n$. As a consequence of our main result, we prove that the submodule of $L_a^2(mathbb{B}_n)$ consisting of functions vanishing on a pure analytic subsets of codimension $1$ is $p$-essentially normal for all $p>n$.
In the spirit of Grothendiecks famous inequality from the theory of Banach spaces, we study a sequence of inequalities for the noncommutative Schwartz space, a Frechet algebra of smooth operators. These hold in non-optimal form by a simple nuclearity argument. We obtain optim
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا