4 problems

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The Fredholm index divisibility conjecture for Rochberg spaces
Let $\mathfrak Z_n$ be the Rochberg space, and let $\mathfrak L(\mathfrak Z_n)$ denote its bounded operators. A Fredholm operator is an operator with finite-dimensional kernel and…
Conjectureopenbanach-spaces fredholm-operators operator-theoryarXiv posted 2 days ago
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Virtanen's Fredholmness conjecture for Toeplitz operators on $H^1$
Virtanen's conjecture. The Toeplitz operator $T_a$ on $H^1(\mathbb{T})$ should be Fredholm.
Conjectureopenfredholm-operators hardy-spaces toeplitz-operatorsarXiv posted 2 days ago
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The Schur coupling index equality conjecture for Fredholm operators
Let $\mathcal X$ and $\mathcal Y$ be Banach spaces. Define $\operatorname{SC}_k(\mathcal X,\mathcal Y)$ as the class of Schur coupling data of index $k$ , and set … The associated i…
Conjectureopenbanach-spaces fredholm-operators functional-analysisarXiv posted 2 days ago
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Index relation conjecture for Fredholm Wiener–Hopf plus Hankel operators
Index relation conjecture. If one of the operators $W(a)+H(b)$ or $W(a)-H(b)$ is Fredholm, then the other is Fredholm as well, and the displayed index relation holds. This would ex…
Conjectureopenfredholm-operators hankel-operators wiener-hopf-operatorsarXiv posted 2 days ago

The Fredholm index divisibility conjecture for Rochberg spaces