Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Hilbert spaces | Statement: [Cameron–Martin theorem, involves, Hilbert spaces]

Target entity: Hilbert spaces
Context triple: [Cameron–Martin theorem, involves, Hilbert spaces]

• A. Hilbert spaces chosen
  Hilbert spaces are complete inner product spaces that provide the fundamental framework for modern functional analysis and many areas of mathematical physics.
• B. Banach spaces
  Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
• C. Gelfand triples (rigged Hilbert spaces)
  Gelfand triples (rigged Hilbert spaces) are a mathematical framework that extends Hilbert spaces to rigorously handle generalized eigenvectors and distributions, particularly in quantum mechanics and functional analysis.
• D. Lebesgue spaces
  Lebesgue spaces are function spaces, denoted \(L^p\), that consist of measurable functions whose absolute values raised to the \(p\)-th power are integrable, forming a fundamental framework in modern analysis and probability theory.
• E. Gelfand–Naimark theorem
  The Gelfand–Naimark theorem is a foundational result in functional analysis that characterizes C*-algebras as algebras of bounded operators on a Hilbert space (and, in the commutative case, as algebras of continuous functions on a locally compact Hausdorff space).
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.