Analytic Hilbert Modules

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Operator Theory and Function Theory in Drury–Arveson Space and Its Quotients (2013, unknown): “s of H2(D) are unitarily equivalent; the following theorem of K. Guo, J. Hu and X. Xu shows that for d≥2, the situation with submodules of H2 d is almost the opposite. Theorem 8.7.1 ([74], Section 5; [41], Section 6). Let Mand Nbe submodules of H2 d , d≥2. Consider the following conditions. (1) Mor ”
The isomorphism problem for some universal operator algebras (2010, background): “The situation in [12] is slightly different, but after a simple modification the proof carries over to our case.”
Essentially Reductive Hilbert Modules II (2006, methodology): “l ring C[z] or an algebra of holomorphic functions. In the case of a function algebra, such modules are called Hilbert modules and their study has been undertaken over the last two decades (cf. [13], [8]). In this paper, we will use the terminology Hilbert module to refer to any module that is a Hil”
Essentially Reductive Hilbert Modules (2004, result): “This generalizes the result of Arveson [4] in which the Hilbert space is the m-shift Hardy space H2m.”
A harmonic analysis approach to essential normality of principal submodules (2011, background): “, zn] with Z(p) ∩ Bn = φ is cyclic which was answered in the affirmative in [8].”