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Everything about Compact operator
Type of continuous linear operator
In functional analysis, a branch of mathematics, a compact operator is a linear operator that behaves, in several important respects, like a finite-dimensional operator such as a matrix. In infinite-dimensional spaces, bounded sets are usually not compact, and bounded sequences need not have convergent subsequences. Compact operators partly restore this finite-dimensional behavior by sending bounded sets to sets whose closures are compact, or equivalently, in normed spaces, by sending bounded sequences to sequences with convergent subsequences. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Compact operatorA 5-minute orientation
- Skim a recent paper: Deep learning-enabled compact optical trigonometric operator with metasurfaceInfluential work since 2022
- Pick up a classic book: Functional analysisThe most-reprinted book on the subject
- Read the landmark paper: Improvement by iteration for compact operator equationsCited 109 times
- Go sideways: Glossary of functional analysisA closely related topic
- Go sideways: Fredholm alternativeA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Improvement by iteration for compact operator equations
Weakly compact operators on operator algebras
The Dirac operator on compact quantum groups
Spectrum of a compact weighted composition operator
Compact exponential product formulas and operator functional derivative
Ergodic actions of compact groups on operator algebras
Weakly compact subsets of symmetric operator spaces
Spectral Synthesis and Operator Synthesis for Compact Groups
🆕 Influential since 2022
Deep learning-enabled compact optical trigonometric operator with metasurface
Compact logic operator utilizing a single-layer metasurface
Development of a compact Ansatz via operator commutativity screening: Digital quantum simulation of molecular systems
Compact neural network modeling of nonlinear dynamical systems via the standard nonlinear operator form
Belonging of Gel’fand integral of positive operator valued functions to separable ideals of compact operators on Hilbert space
📚 Books worth reading
Functional analysisS. Kesavan · 2009
The Rough Guide to OperaMatthew Boyden · 2002
Compact non-self-adjoint operatorsJohn R. Ringrose · 1971- 📕Pseudodifferential analysis on conformally compact spacesRobert Lauter · 2003
- 📕Limit operators, collective compactness, and the spectral theory of infinite matricesSimon N. Chandler-Wilde · 2010
- 📕La propriété (T) de Kazhdan pour les groupes localement compactsPierre de La Harpe · 1989
Advanced color correction and effects in Final Cut Pro 5.Alexis Van Hurkman, DigitalFilm Tree · 2005- 📕Interpolation of compact operators in the multidimensional caseNicolae Cofan · 2003
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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