On the index of invariant subspaces in spaces of analytic functions of several complex variables

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Quotients of standard Hilbert modules (2005, unknown): “Similarly, submodules and quotients of essentially normal Hilbert modules need not be essentially normal in general (some ungraded examples are exhibited in [GS05]).”
Operator Theory and Function Theory in Drury–Arveson Space and Its Quotients (2013, unknown): “x of a Fredholm tuple (for more details on spectral theory and Fredholm theory of commuting d-tuples, see the chapter on multiparameter spectral theory by V. Mu¨ller in this Handbook). Theorem 9.5.1 ([72], Theorem 4.5). Let T be a pure d-contraction of ﬁnite rank. Denote the essential spectrum of T ”
Essentially normal Hilbert modules and K-homology (2008, background): “Applying [33] again, it holds that Z(I ) ∩ Bd ⊆ σ(S1, .”
On the Isomorphism Problem for Multiplier Algebras of Nevanlinna-Pick Spaces (2015, methodology): “(iv) _e idea to use the factorization theorem to solve Gleason’s problem in Mult(H) appears in [21],where thiswas done for themultiplier algebra of the Drury– Arveson space.”