Formal Reproducing Kernel Hilbert Spaces: The Commutative and Noncommutative Settings

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Classes of tuples of commuting contractions satisfying the multivariable von Neumann inequality (2009, unknown): “Since not resorting to this formalism in full, we will only need a definition and some basic facts (for more details, see [11] and [14, Section 2]).”
Matrix-J-unitary Non-commutative Rational Formal Power Series (2004, methodology): “Vinnikov introduce non-commutative formal reproducing kernel Hilbert spaces (NFRKHS for short) in [14].”
Noncommutative reproducing kernel Hilbert spaces (2016, background): “onary between the global/nc functional reproducing kernel Hilbert spaces being discussed here and the notion of formal nc reproducing kernel Hilbert spaces introduced by two of the present authors in [14]. Toward this end, we ﬁrst need to review the setup from [14]. We let F+ d be the monoid on dgen”