Examples of 'banach spaces' in a sentence
Meaning of "banach spaces"
Banach spaces are mathematical structures in functional analysis that satisfy certain properties related to vector spaces and norms. They are named after the Polish mathematician Stefan Banach and are widely used in the study of mathematical analysis and other branches of mathematics
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- plural of Banach space
How to use "banach spaces" in a sentence
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banach spaces
Banach spaces play a central role in functional analysis.
To do so we first study continuous multilinear mappings and homogeneous polynomials between banach spaces.
Banach spaces are a different generalization of Hilbert spaces.
A counterexample to the approximation problem in Banach spaces.
Suppose that and are Banach spaces and that.
This applies in particular to separable reflexive Banach spaces.
Banach spaces are much more complicated than Hilbert spaces.
This is in stark contrast to the situation in Banach spaces.
Measures that take values in Banach spaces have been studied extensively.
Most of functional analysis is formulated for Banach spaces.
A convexity condition in Banach spaces and the strong law of large numbers.
Handbook of the geometry of Banach spaces.
Some generalizations to Banach spaces and more general topological vector spaces are possible.
It is necessary that the spaces in question be Banach spaces.
Any general property of Banach spaces continues to hold for Hilbert spaces.
See also
Schatten widely studied tensor products of Banach spaces.
A geometrical characterization of Banach spaces with the Radon-Nikodym property.
One has the isometric isomorphism of Banach spaces.
There are no Banach spaces that are nuclear, except for the finite-dimensional ones.
Of special interest are complete normed spaces called Banach spaces.
We describe next the geometricproperties of Banach spaces which intervene in our results.
The definition of weak convergence can be extended to Banach spaces.
This results in an important property of Banach spaces known as the Radon-Nikodym property.
Closed linear operators are a class of linear operators on Banach spaces.
Direct sum of Banach spaces.
One can also study the spectral properties of operators on Banach spaces.
Two prominent examples occur for Banach spaces and Hilbert spaces.
His research focuses predominantly on functional analysis and the geometry of Banach spaces.
It is a general fact that compact operators on Banach spaces have only discrete spectrum.
The topic of this dissertation is the geometric and isometric theory of Banach spaces.
More generally, all uniformly convex Banach spaces are reflexive according to the Milman-Pettis theorem.
The ℓp spaces can be embedded into many Banach spaces.
Kachurovskii 's theorem shows that convex functions on Banach spaces have monotonic operators as their derivatives.
Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces.
The category of Banach spaces.
She proved the equivalence of the zero measure notions of infinite dimensional Banach spaces.
A further generalization for a function between Banach spaces is the Fréchet derivative.
The second decomposition generalizes more easily for general compact operators on Banach spaces.
The construction may also be extended to Banach spaces and Hilbert spaces.
His formulation works for Bochner integral Lebesgue integral for mappings taking values in Banach spaces.
Interpolation of Banach spaces.
This is useful in showing the non-existence of certain measures on infinite-dimensional Banach spaces.
Using the tree-characterization, Enflo proved that super-reflexive Banach spaces admit an equivalent uniformly convex norm.
These questions are closely related with the Lipschitz classification of Banach spaces.
Convex-transitive Banach spaces and their hyperplanes.
Reflexive normed spaces are Banach spaces.
They are Banach spaces in general and Hilbert spaces in the special case " p " 2.
Such spaces are called Banach spaces.
Also, the notion of derivative can be extended to arbitrary functions between Banach spaces.
Finite dimensional Banach spaces are K-spaces.
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Uniformly convex banach space
Banach spaces play a central role in functional analysis
