Nuclear Operator
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Nuclear Operator
In mathematics, nuclear operators are an important class of linear operators introduced by Alexander Grothendieck Alexander Grothendieck (; ; ; 28 March 1928 – 13 November 2014) was a mathematician who became the leading figure in the creation of modern algebraic geometry. His research extended the scope of the field and added elements of commutative ... in his doctoral dissertation. Nuclear operators are intimately tied to the projective tensor product The strongest locally convex topological vector space (TVS) topology on X \otimes Y, the tensor product of two locally convex TVSs, making the canonical map \cdot \otimes \cdot : X \times Y \to X \otimes Y (defined by sending (x, y) \in X \times Y ... of two topological vector spaces (TVSs). Preliminaries and notation Throughout let ''X'',''Y'', and ''Z'' be topological vector spaces (TVSs) and ''L'' : ''X'' → ''Y'' be a linear operator (no assumption of continuity is made unless otherwise stated). * The projectiv ...
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Alexander Grothendieck
Alexander Grothendieck (; ; ; 28 March 1928 – 13 November 2014) was a mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained ( ... who became the leading figure in the creation of modern algebraic geometry Algebraic geometry is a branch of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and thei .... His research extended the scope of the field and added elements of commutative algebra Commutative algebra is the branch of algebra Algebra (from ar, الجبر, lit=reunion of broken parts, bonesetting, translit=al-jabr) is one of the areas of mathematics, broad areas of mathematics, together with number t ...
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