query: Closed subspace $M=(M^{\perp})^{\perp}$ in PRE hilbert spaces.
positive_passages.docid: 21459
positive_passages.text: Orthogonal complement examples
negative_passages.docid: 130045
negative_passages.text: Show that $l^2$ is a Hilbert space
negative_passages.docid: 90525
negative_passages.text: The subspace of $\ell_2$
negative_passages.docid: 55533
negative_passages.text: Tensor Product: Hilbert Spaces
negative_passages.docid: 19946
negative_passages.text: Let $W$ be a given subspace of $V$ find the orthogonal complement $W^{\perp}$
negative_passages.docid: 134065
negative_passages.text: A question about an $n$-dimensional subspace of $\mathbb{F}^{S}$.
negative_passages.docid: 125623
negative_passages.text: Subspaces of separable normed spaces
negative_passages.docid: 59055
negative_passages.text: Diagonalizable transformation restricted to an invariant subspace is diagonalizable
negative_passages.docid: 64840
negative_passages.text: A Banach space that is not a Hilbert space
negative_passages.docid: 59531
negative_passages.text: Do $T$-invariant subspaces necessarily have a $T$-invariant complement?
negative_passages.docid: 57609
negative_passages.text: Hahn-Banach proof by extension of basis
negative_passages.docid: 116632
negative_passages.text: Gram-Schmidt in Hilbert space?
negative_passages.docid: 46698
negative_passages.text: Showing a set is closed under inverses
negative_passages.docid: 37953
negative_passages.text: Primary Decomposition of $\mathbb{R^n}$ under T
negative_passages.docid: 120766
negative_passages.text: Prove ${y_n}$ is a basis for a Hilbert space $H$.
negative_passages.docid: 17159
negative_passages.text: Proof of Closest Point Theorem in Hilbert Space
negative_passages.docid: 82355
negative_passages.text: When is the image of a linear operator (between Banach spaces) closed?