Trace ideal criteria for Toeplitz operators

Finite Rank Bergman–Toeplitz and Bargmann–Toeplitz Operators in Many Dimensions

“…If the operator (Bargmann or Bergman) is zero than the measure should be zero, and it follows easily from Stone-Weierstrass theorem. In 1987 in [4] a proof was proposed of the finite rank conjecture for d = 1, but it was seriously flowed. In 2002 an attempt to prove this conjecture, again for d = 1, was made by N. Das in [1], however, again, with incorrigible mistakes, see the review [2].…”

Schatten class Toeplitz operators on weighted Bergman spaces of tube domains over symmetric cones

“…Schatten class S p ( 0 < p ≤ ∞ ) criteria of the Toeplitz operators have been obtained by several authors on bounded domains of C n (see [1,8,12,21,22] and the references therein). For unbounded domains, Schatten classes have been also characterized in Fock spaces by several authors (see for example [11,14] and the references therein).…”

“…Our aim here is to extend this result to the range 1 ≤ p < 2 . We refer to [8,12,21,22] for the corresponding results on some classical domains.…”

Вложения Модельных Подпространств Класса Харди: Компактность И Идеалы Шаттена - Фон Неймана

“…Наши условия, сформулированные в терминах диадического разбиения кру-га, аналогичны теореме Люкинга [21], описывающей вложения класса S r всего пространства Харди, а также результатам Парфенова [22], [23]. Дальнейшее обсуждение этих результатов см.…”

“…, 2 n − 1. Напомним принадлежащую Люкингу [21] теорему, описывающую S r -свойст-ва вложений всего класса Харди…”