TL;DR
This paper investigates whether the product of two nuclear operators in Banach spaces can be factored through a trace class operator in a Hilbert space, providing a negative answer to a question posed by Boris Mitjagin.
Contribution
The paper offers a counterexample showing that such a factorization is not always possible, clarifying the limitations of nuclear operator products.
Findings
Counterexample disproves the factorization possibility
Clarifies the relationship between nuclear and trace class operators
Answers a specific open question in operator theory
Abstract
We answer in negative to the following question of Boris Mitjagin: Is it true that a product of two nuclear operators in Banach spaces can be factored through a trace class operator in a Hilbert space?
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Banach Space Theory · Spectral Theory in Mathematical Physics