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essentially bounded

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  • Bounded mean oscillation — In harmonic analysis, a function of bounded mean oscillation, also known as a BMO function, is a real valued function whose mean oscillation is bounded (finite). The space of functions of bounded mean oscillation (BMO), is a function space that,… …   Wikipedia

  • Essential range — In mathematics, particularly measure theory, the essential range of a function is intuitively the non negligible range of the function. One way of thinking of the essential range of a function is the set on which the range of the function is most …   Wikipedia

  • Von Neumann algebra — In mathematics, a von Neumann algebra or W* algebra is a * algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. They were originally introduced by John von Neumann,… …   Wikipedia

  • Decomposition of spectrum (functional analysis) — In mathematics, especially functional analysis, the spectrum of an operator generalizes the notion of eigenvalues. Given an operator, it is sometimes useful to break up the spectrum into various parts. This article discusses a few examples of… …   Wikipedia

  • Lp space — In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p norm for finite dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford Schwartz 1958, III.3),… …   Wikipedia

  • Direct integral — In mathematics and functional analysis a direct integral is a generalization of the concept of direct sum. The theory is most developed for direct integrals of Hilbert spaces and direct integrals of von Neumann algebras. The concept was… …   Wikipedia

  • Amenable group — In mathematics, an amenable group is a locally compact topological group G carrying a kind of averaging operation on bounded functions that is invariant under left (or right) translation by group elements. The original definition, in terms of a… …   Wikipedia

  • Crossed product — In mathematics, and more specifically in the theory of von Neumann algebras, a crossed product is a basic method of constructing a new von Neumann algebra from a von Neumann algebra acted on by a group. It is related to the semidirect product… …   Wikipedia

  • Self-adjoint operator — In mathematics, on a finite dimensional inner product space, a self adjoint operator is one that is its own adjoint, or, equivalently, one whose matrix is Hermitian, where a Hermitian matrix is one which is equal to its own conjugate transpose.… …   Wikipedia

  • Italy — /it l ee/, n. a republic in S Europe, comprising a peninsula S of the Alps, and Sicily, Sardinia, Elba, and other smaller islands: a kingdom 1870 1946. 57,534,088; 116,294 sq. mi. (301,200 sq. km). Cap.: Rome. Italian, Italia. * * * Italy… …   Universalium

  • Africa — /af ri keuh/, n. 1. a continent S of Europe and between the Atlantic and Indian oceans. 551,000,000; ab. 11,700,000 sq. mi. (30,303,000 sq. km). adj. 2. African. * * * I Second largest continent on Earth. It is bounded by the Mediterranean Sea,… …   Universalium

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