We study non-linear traces of the Choquet type and Sugeno on algebra compact operators. They have certain partial additivities. show that these additivities characterize both respectively. There exists a close relation between majorization theory. trace class operators for type. More generally we discuss Schatten–von Neumann p-class determine when they form Banach spaces. This is an attempt at ...

In this paper, we completely characterize the compactness of Volterra type integration operators $$J_b$$ acting from weighted Bergman spaces $$A^p_{\alpha }$$ to Hardy $$H^q$$ for all $$0<p,q<\infty $$ . Furthermore, give some estimates essential norms $$J_b:A^p_{\alpha }\rightarrow H^q$$ in case $$0<p\le q<\infty We finally describe membership Schatten(-Herz) class operators.

In this paper, we focus on the weighted Bergman spaces Aφp in D with φ∈W0. We first give characterizations of those finite positive Borel measures µ such that embedding Aφp⊂Lμq is bounded or compact for 0<p,q<∞. Then describe Toeplitz operators Tμ from one space to another Aφq all possible Finally, characterize Schatten class Aφ2.

Our first aim is to clarify the results obtained by Lidskii devoted decomposition on root vector system of non-selfadjoint operator. We use a technique entire function theory and introduce so-called Schatten–von Neumann class convergence exponent. Considering strictly accretive operators satisfying special conditions formulated in terms norm, we construct sequence contours power type that contr...