From the 1 of 10 linked papers with an AI index.
10 papers
Trace formulas for -perturbations and extension of Koplienko-Neidhardt trace formulas
Arup Chattopadhyay, Clément Coine, Saikat Giri +1
The paper broadens the class of functions for which second‑order trace formulas hold for Hilbert‑Schmidt perturbations and establishes modified trace formulas for Schatten‑p pertur…
Finite sum of squares, finite realization and noncommutative Carathéodory approximation
Tirthankar Bhattacharyya, James Eldred Pascoe, Chandan Pradhan
In the noncommutative polydisc, we first prove a positive sum of squares formula for a non-negative hereditary rational nc-function. The number of summands is finite. This result i…
Trace formulas in higher dimensions
Arup Chattopadhyay, Saikat Giri, Chandan Pradhan +1
The paper establishes the Krein and Koplienko trace formulas for multivariable operator functions on symmetrically normed ideals of bounded operators. Results are proved for self-a…
Isometric Embeddability of Schatten Classes Revisited
Arup Chattopadhyay, Chandan Pradhan, Anna Skripka
In this note, we summarize known results and open questions on the existence of isometric embeddings between different Schatten classes as well as obtain a new non-embeddability re…
Differentiation, Taylor series, and all order spectral shift functions, for relatively bounded perturbations
Arup Chattopadhyay, Teun D. H. van Nuland, Chandan Pradhan
Given self-adjoint, symmetric and relatively -bounded, and satisfying mild conditions, we show that the Gateaux derivative $$\frac{d^n}{dt^n}…
Noncommutative -differentiability and trace formulae
Arup Chattopadhyay, Clément Coine, Saikat Giri +1
Let be a semifinite von Neumann algebra equipped with a normal faithful semifinite trace , and let denote the associated noncommutative -s…