Introduction to Operator Theory and Invariant Subspaces

By B. Beauzamy. 2012

113 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/7c763d699225120dce65304cc15752949ffa80b6

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In Applied Mathematics

In Mechanical Engineering

Citations in the corpus

Expansivity and Shadowing in Linear Dynamics (2016, background): “For example, Beauzamy [4] and Prǎjiturǎ [28] constructed examples of completely irregular operators on the Hilbert space l2.”
Distributional chaos for linear operators (2013, background): “The following concept is a generalization to Fréchet spaces of the one introduced by Beauzamy [5] for Banach spaces (see [7]).”
Switching Stabilization for a Class of Slowly Switched Systems (2015, background): “Lemma 2: [2] For any subspaces S1, S2, S1 ∩ S2 is also a subspace.”
A Course in Functional Analysis and Measure Theory (2018, background): “, the monograph [2] and the surveys [45, 71]).”
Distributional chaos for operators with full scrambled sets (2013, unknown): “We recall from [3] that a vector x ∈ X is said to be irregular for an operator T if lim infn→∞ ‖Tx‖ = 0, while lim supn→∞ ‖Tx‖ =∞.”
Linear subsets of nonlinear sets in topological vector spaces (2013, background): “Inspired by this concept and by the notion of irregular vector coined by Beauzamy [56] (if X is a Banach space and x0 ∈ X, an operator T ∈ L(X) is called irregular, provided that the sequence (Tnx0) is unbounded but it has a subsequence tending to 0), the authors of [57] presented the following conc”
Li–Yorke chaos in linear dynamics (2014, methodology): “Li–Yorke and dense Li–Yorke chaos The following concept is a generalization to Fréchet spaces of that introduced by Beauzamy [4] for Banach spaces.”
Li–Yorke and distributionally chaotic operators (2010, background): “→ X a bounded operator. In this case the associated distance is d(x,y) = kx − yk, with x,y ∈ X, where k·k is the norm of X. We recall the following concept from operator theory. Deﬁnition 3 (Beauzamy [3]). A vector x ∈ X is said to be irregular for T if liminfnkTnxk = 0 and limsupnkTnxk = ∞. Inspire”