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2. Riesz's lemma - Wikipedia

   en.wikipedia.org/wiki/Riesz's_lemma

   However, every finite dimensional normed space is a reflexive Banach space, so Riesz’s lemma does holds for = when the normed space is finite-dimensional, as will now be shown. When the dimension of X {\displaystyle X} is finite then the closed unit ball B ⊆ X {\displaystyle B\subseteq X} is compact.

3. Orthogonality (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Orthogonality_(mathematics)

   In Euclidean space, two vectors are orthogonal if and only if their dot product is zero, i.e. they make an angle of 90° (radians), or one of the vectors is zero. [4] Hence orthogonality of vectors is an extension of the concept of perpendicular vectors to spaces of any dimension.

4. Lp space - Wikipedia

   en.wikipedia.org/wiki/Lp_space

   The Lebesgue space. The normed vector space ((,), ‖ ‖) is called space or the Lebesgue space of -th power integrable functions and it is a Banach space for every (meaning that it is a complete metric space, a result that is sometimes called the Riesz–Fischer theorem).

5. Hilbert–Schmidt operator - Wikipedia

   en.wikipedia.org/wiki/Hilbert–Schmidt_operator

   The space of all bounded linear operators of finite rank (i.e. that have a finite-dimensional range) is a dense subset of the space of Hilbert–Schmidt operators (with the Hilbert–Schmidt norm). [4] The set of Hilbert–Schmidt operators is closed in the norm topology if, and only if, H is finite-dimensional.

6. Norm (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Norm_(mathematics)

   A vector space with a specified norm is called a normed vector space. In a similar manner, a vector space with a seminorm is called a seminormed vector space. The term pseudonorm has been used for several related meanings. It may be a synonym of "seminorm". [1]

7. Riesz–Fischer theorem - Wikipedia

   en.wikipedia.org/wiki/Riesz–Fischer_theorem

   The Riesz–Fischer theorem also applies in a more general setting. Let R be an inner product space consisting of functions (for example, measurable functions on the line, analytic functions in the unit disc; in old literature, sometimes called Euclidean Space), and let {} be an orthonormal system in R (e.g. Fourier basis, Hermite or Laguerre polynomials, etc. – see orthogonal polynomials ...

8. Download, install, or uninstall AOL Desktop Gold

   help.aol.com/articles/aol-desktop-downloading...

   Learn how to download and install or uninstall the Desktop Gold software and if your computer meets the system requirements.

9. Orlicz space - Wikipedia

   en.wikipedia.org/wiki/Orlicz_space

   The spaces are named for Władysław Orlicz, who was the first to define them in 1932. Besides the L p spaces, a variety of function spaces arising naturally in analysis are Orlicz spaces. One such space L log + L, which arises in the study of Hardy–Littlewood maximal functions, consists of measurable functions f such that the