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7 relations: Bounded operator, Functional analysis, Jacob T. Schwartz, Limit of a sequence, Lp space, Mathematics, Nelson Dunford.
Bounded operator
In functional analysis, a bounded linear operator is a linear transformation L between normed vector spaces X and Y for which the ratio of the norm of L(v) to that of v is bounded above by the same number, over all non-zero vectors v in X. In other words, there exists some M\ge 0 such that for all v in X The smallest such M is called the operator norm \|L\|_ \, of L. A bounded linear operator is generally not a bounded function; the latter would require that the norm of L(v) be bounded for all v, which is not possible unless L(v).
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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.
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Jacob T. Schwartz
Jacob Theodore "Jack" Schwartz (January 9, 1930 – March 2, 2009) was an American mathematician, computer scientist, and professor of computer science at the New York University Courant Institute of Mathematical Sciences.
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Limit of a sequence
As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.
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Lp space
In mathematics, the Lp spaces are function spaces defined using a natural generalization of the ''p''-norm for finite-dimensional vector spaces.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Nelson Dunford
Nelson James Dunford (December 12, 1906 – September 7, 1986) was an American mathematician, known for his work in functional analysis, namely integration of vector valued functions, ergodic theory, and linear operators.
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