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Vitold Shmulyan
Vitold Lvovich Shmulyan (russian: Витольд Львович Шмульян, 29 August 1914 – 27 August 1944) was a Soviet mathematician known for his work in functional analysis. The Eberlein–Šmulian theorem and Krein–Smulian theorem In mathematics, particularly in functional analysis, the Krein-Smulian theorem can refer to two theorems relating the closed convex hull and compactness in the weak topology In mathematics, weak topology is an alternative term for certain ini ... are named after him. Notes {{DEFAULTSORT:Shmulian, Vitold Functional analysts Soviet mathematicians 1914 births 1944 deaths ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view turned out to be particularly useful for the study of differential and integral equations. The usage of the word '' functional'' as a noun goes back to the calculus of variations, implying a function whose argument is a function. The term was first used in Hadamard's 1910 book on that subject. However, the general concept of a functional had previously been introduced in 1887 by the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eberlein–Šmulian Theorem
In the mathematical field of functional analysis, the Eberlein–Šmulian theorem (named after William Frederick Eberlein and Witold Lwowitsch Schmulian) is a result that relates three different kinds of weak compactness in a Banach space. Statement Eberlein–Šmulian theorem: If ''X'' is a Banach space and ''A'' is a subset of ''X'', then the following statements are equivalent: # each sequence of elements of ''A'' has a subsequence that is weakly convergent in ''X'' # each sequence of elements of ''A'' has a weak cluster point in ''X'' # the weak closure of ''A'' is weakly compact. A set ''A'' can be weakly compact in three different ways: * Sequential compactness: Every sequence from ''A'' has a convergent subsequence whose limit is in ''A''. * Limit point compactness: Every infinite subset of ''A'' has a limit point in ''A''. * Compactness (or Heine- Borel compactness): Every open cover of ''A'' admits a finite subcover. The Eberlein–Šmulian theorem states that the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Krein–Smulian Theorem
In mathematics, particularly in functional analysis, the Krein-Smulian theorem can refer to two theorems relating the closed convex hull and compactness in the weak topology In mathematics, weak topology is an alternative term for certain initial topologies, often on topological vector spaces or spaces of linear operators, for instance on a Hilbert space. The term is most commonly used for the initial topology of a .... They are named after Mark Krein and Vitold Shmulyan, who published them in 1940. Statement Both of the following theorems are referred to as the Krein-Smulian Theorem. See also * * References Bibliography * * * * * {{Mathanalysis-stub Banach spaces Topological vector spaces Theorems in functional analysis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Functional Analysts
Functional may refer to: * Movements in architecture: ** Functionalism (architecture) ** Form follows function * Functional group, combination of atoms within molecules * Medical conditions without currently visible organic basis: ** Functional symptom ** Functional disorder * Functional classification for roads * Functional organization * Functional training In mathematics * Functional (mathematics), a term applied to certain scalar-valued functions in mathematics and computer science ** Functional analysis ** Linear functional, a type of functional often simply called a functional in the context of functional analysis * Higher-order function, also called a functional, a function that takes other functions as arguments In computer science, software engineering * (C++), a header file in the C++ Standard Library * Functional design, a paradigm used to simplify the design of hardware and software devices * Functional model, a structured representation of functions, activit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soviet Mathematicians
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national republics; in practice, both its government and its economy were highly centralized until its final years. It was a one-party state governed by the Communist Party of the Soviet Union, with the city of Moscow serving as its capital as well as that of its largest and most populous republic: the Russian SFSR. Other major cities included Leningrad (Russian SFSR), Kiev (Ukrainian SSR), Minsk (Byelorussian SSR), Tashkent (Uzbek SSR), Alma-Ata (Kazakh SSR), and Novosibirsk (Russian SFSR). It was the largest country in the world, covering over and spanning eleven time zones. The country's roots lay in the October Revolution of 1917, when the Bolsheviks, under the leadership of Vladimir Lenin, overthrew the Russian Provisional Government that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1914 Births
This year saw the beginning of what became known as World War I, after Archduke Franz Ferdinand of Austria, heir to the Austrian throne was assassinated by Serbian nationalist Gavrilo Princip. It also saw the first airline to provide scheduled regular commercial passenger services with heavier-than-air aircraft, with the St. Petersburg–Tampa Airboat Line. Events January * January 1 – The St. Petersburg–Tampa Airboat Line in the United States starts services between St. Petersburg and Tampa, Florida, becoming the first airline to provide scheduled regular commercial passenger services with heavier-than-air aircraft, with Tony Jannus (the first federally-licensed pilot) conveying passengers in a Benoist XIV flying boat. Abram C. Pheil, mayor of St. Petersburg, is the first airline passenger, and over 3,000 people witness the first departure. * January 11 – The Sakurajima volcano in Japan begins to erupt, becoming effusive after a very large eart ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
