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Twisted Hilbert and complexity in Banach spaces

Grant number: 18/03765-1
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): May 01, 2018
Effective date (End): March 23, 2020
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Valentin Raphael Henri Ferenczi
Grantee:Willian Hans Goes Corrêa
Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:16/25574-8 - Geometry of Banach Spaces, AP.TEM
Associated scholarship(s):19/09205-0 - Applications of Functional Analysis to Quantum Information Theory, BE.EP.PD

Abstract

A twisted sum of two Banach spaces Y and Z is a quasi-Banach space X which has a subspace isomorphic to Y with respective quotient isomorphic to Z. When Y and Z are Hilbert spaces X is said to be a twisted Hilbert. Few examples of twisted Hilbert are known, and in this project we intend to find other examples, conditions for singularity (Y being the most non-complemented in X) e for other properties of interest. Among them is if the isomorphism class of X is a Borel class.

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Scientific publications (7)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
CASTILLO, JESUS M. F.; CORREA, WILLIAN H. G.; FERENCZI, VALENTIN; GONZALEZ, MANUEL. Differential processes generated by two interpolators. REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, v. 114, n. 4, . (15/17216-1, 18/03765-1, 16/25574-8, 13/11390-4)
GOES CORREA, WILLIAN HANS. Complex interpolation of families of Orlicz sequence spaces. Israel Journal of Mathematics, v. 240, n. 2, p. 603-624, . (18/03765-1, 16/25574-8)
CABELLO SANCHEZ, FELIX; CASTILLO, JESUS M. F.; CORREA, WILLIAN H. G.; FERENCZI, VALENTIN; GARCIA, RICARDO. On the Ext(2)-problem for Hilbert spaces. JOURNAL OF FUNCTIONAL ANALYSIS, v. 280, n. 4, . (18/03765-1, 16/25574-8)
CASTILLO, JESUS M. F.; CORREA, WILLIAN H. G.; FERENCZI, VALENTIN; GONZALEZ, MANUEL. ON THE STABILITY OF THE DIFFERENTIAL PROCESS GENERATED BY COMPLEX INTERPOLATION. JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, v. 21, n. 1, p. 303-334, . (13/11390-4, 18/03765-1, 15/17216-1, 16/25574-8)
SANCHEZ, FELIX CABELLO; CASTILLO, JESUS M. F.; CORREA, WILLIAN H. G.. Higher order derivatives of analytic families of Banach spaces. STUDIA MATHEMATICA, v. N/A, p. 53-pg., . (18/03765-1, 16/25574-8, 21/13401-0)
CORREA, WILLIAN H. G.; LAMI, LUDOVICO; PALAZUELOS, CARLOS. Maximal Gap Between Local and Global Distinguishability of Bipartite Quantum States. IEEE TRANSACTIONS ON INFORMATION THEORY, v. 68, n. 11, p. 9-pg., . (16/25574-8, 19/09205-0, 18/03765-1)
CORREA, WILLIAN H. G.. COMPLEX INTERPOLATION OF ORLICZ SEQUENCE SPACES AND ITS HIGHER ORDER ROCHBERG SPACES. HOUSTON JOURNAL OF MATHEMATICS, v. 48, n. 1, p. 14-pg., . (18/03765-1, 16/25574-8, 19/09205-0)

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