Results 31 to 40 of about 49,185 (121)

On invariant subspaces of a linear operator

We discuss the concept of invariant subspaces for unbounded linear operators, point out some shortcomings of known definitions, and propose our own.
Belishev, M. I., Simonov, S. A.
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Finite dimensional invariant subspaces for a semigroup of linear operators

Journal of Mathematical Analysis and Applications, 1983
The left-amenability of a semitopological semigroup S is characterized by the existence of an invariant n-dimensional subspace of certain representations of S. This is a generalizatin of a result of \textit{K. Fan} [Indagationes Math. 27, 447-451 (1965; Zbl 0139.311)].
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Weighted Hardy spaces: shift invariant and coinvariant subspaces, linear systems and operator model theory

, 2013
The Sz.-Nagy--Foias model theory for $C_{\cdot 0}$ contraction operators combined with the Beurling-Lax theorem establishes a correspondence between any two of four kinds of objects: shift-invariant subspaces, operator-valued inner functions ...
Ball, Joseph A., Bolotnikov, Vladimir
core  

On linear operators with an invariant subspace of functions

, 2004
6 pages, LaTeX, discussion extended, reference ...
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Characterization of invariant subspaces for a nilpotent linear operator that admit complementary invariant subspaces

The Electronic Journal of Linear Algebra
The aim of this work is to solve the problem of determining the necessary and sufficient conditions for a vector subspace invariant by a nilpotent endomorphism to admit a complementary invariant subspace for the same linear operator. As applications, we offer results about Jordan bases associated with nilpotent linear maps and reflexive generalized ...
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The number of invariant subspaces under a linear operator on finite vector spaces

Advances in Mathematics of Communications, 2011
Let $V$ be an $n$-dimensional vector space over the finite field $\mathbb F$q and $T$ a linear operator on $V$. For each $k\in\{1,\ldots,n\}$ we determine the number of $k$-dimensional $T$-invariant subspaces of $V$. Finally, this method is applied for the enumeration of all monomially nonisometric linear $(n,k)$-codes over $\mathbb F$q.
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Operators associated with the soft and hard spectral edges of unitary ensembles

, 2006
Using Hankel operators and shift-invariant subspaces on Hilbert space, this paper develops the theory of the operators associated with soft and hard edges of eigenvalue distributions of random matrices. Tracy and Widom introduced a projection operator $W$
Blower, Gordon
core  

On the orbit of invariant subspaces of linear operators in finite-dimensional spaces (new proof of a Halmos's result)

Linear Algebra and its Applications, 2001
The fact that for any linear operator \(A\) on a finite-dimensional complex vector space, the lattice of invariant subspaces of \(A\) coincides with the set of ranges of the operators which commute with \(A\), was pointed out by \textit{P. R. Halmos} [Linear Algebra Appl. 4, 11-15 (1971; Zbl 0264.15001)].
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Characterization of finite dimensional subspaces of complex functions that are invariant under linear differential operators

, 2016
The method to solve inhomogeneous linear differential equations that is usually taught at school relies on the fact that the right hand side function is the product of a polynomial and an exponential and that the linear spaces of those functions are invariant under differential operators (finite or ordinary).
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Invariant subspaces of certain linear operators [PDF]

Bulletin of the American Mathematical Society, 1963
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