query: Characterization of Hilbert spaces
positive_passages.docid: 156855
positive_passages.text: separable Banach space with Banach-Mazur distances to $\ell_2^n$ bounded must be isomorphic to $\ell_2$?
negative_passages.docid: 28731
negative_passages.text: Banach space in functional analysis
negative_passages.docid: 65346
negative_passages.text: Characterisation of uniformly continuous function
negative_passages.docid: 61484
negative_passages.text: Continuously invertible operators
negative_passages.docid: 14550
negative_passages.text: Every Hilbert space has an orthonomal basis - using Zorn's Lemma
negative_passages.docid: 34173
negative_passages.text: Banach spaces and their unit sphere
negative_passages.docid: 128361
negative_passages.text: The kernel and range of the powers of a self-adjoint operator
negative_passages.docid: 156727
negative_passages.text: A step in the proof of Characterization of $W^{1,\infty}$
negative_passages.docid: 14166
negative_passages.text: Hilbert space of harmonic oscillator: Countable vs uncountable?
negative_passages.docid: 81471
negative_passages.text: Finite dimensional spaces
negative_passages.docid: 15839
negative_passages.text: equivalent norms in Banach spaces of infinite dimension
negative_passages.docid: 129549
negative_passages.text: Showing that the orthogonal projection in a Hilbert space is compact iff the subspace is finite dimensional
negative_passages.docid: 73790
negative_passages.text: Are two Hilbert spaces with the same algebraic dimension (their Hamel bases have the same cardinality) isomorphic?
negative_passages.docid: 47031
negative_passages.text: Isometric to Dual implies Hilbertable?
negative_passages.docid: 114510
negative_passages.text: Inner Product Spaces
negative_passages.docid: 151046
negative_passages.text: Closure of the invertible operators on a Banach space
negative_passages.docid: 57609
negative_passages.text: Hahn-Banach proof by extension of basis