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Everything about Bounded operator
Kind of linear transformation
In functional analysis and operator theory, a bounded linear operator is a special kind of linear transformation that is particularly important in infinite dimensions. In finite dimensions, a linear transformation takes a bounded set to another bounded set. However, in infinite dimensions, linearity is not enough to ensure that bounded sets remain bounded: a bounded linear operator is thus a linear transformation that sends bounded sets to bounded sets. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Bounded operatorA 5-minute orientation
- Skim a recent paper: Robust Nonlinear FIR Filtering via Koopman Operator Framework With Combined Bounded-Gaussian Noise CharacterizationInfluential work since 2022
- Pick up a classic book: Einführung in die Methode Branch and BoundThe most-reprinted book on the subject
- Read the landmark paper: On the numerical range of a bounded operator.Cited 75 times
- Go sideways: Bornological spaceA closely related topic
- Go sideways: Continuous linear operatorA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
On the numerical range of a bounded operator.
A bounded operator approach to Tomita-Takesaki theory
Eigenvalue problems of Ginzburg–Landau operator in bounded domains
On the logarithm of a uniformly bounded operator
THE CESÀRO OPERATOR ON BOUNDED ANALYTIC FUNCTIONS
A power-bounded operator that is not polynomially bounded.
A completely bounded characterization of operator algebras
Completely bounded homomorphisms of operator algebras
🆕 Influential since 2022
Robust Nonlinear FIR Filtering via Koopman Operator Framework With Combined Bounded-Gaussian Noise Characterization
Euclidean Operator Radius Inequalities of a Pair of Bounded Linear Operators and Their Applications
The Stokes operator in two-dimensional bounded Lipschitz domains
Solvability of (λ, μ)-Commuting Operator Equations for Bounded Generalization of Hyponormal Operators
Bounded Solutions of a Differential Equation with Piecewise Constant Operator Coefficients
📚 Books worth reading
Einführung in die Methode Branch and BoundFranz Weinberg · 1968
Differentiability of six operators on nonsmooth functions and p-variationR. M. Dudley · 1999- 📕A note on multiactivity multifacility systems by branch and boundBasheer M. Khumawala · 1974
- 📕Branch and boundFranz Weinberg · 1973
- 📕Recent Progress on Operator Theory and Approximation in Spaces of Analytic FunctionsCatherine Beneteau, Alberto A. Condori · 2017
- 📕Spectral geometryInternational Conference on Spectral Geometry (2010 Dartmouth College) · 2012
Imaging, multi-scale, and high-contrast partial differential equationsHabib Ammari · 2016- 📕Trends in harmonic analysis and its applicationsJens Gerlach Christensen · 2015
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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