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Linear Spaces and Linear Operators
1986The present chapter is concerned with the basic setting for a great deal of modern mathematical analysis and applied mathematics: the linear or vector space. In a linear space, addition, subtraction, magnification and contraction of elements are all possible, and sometimes even multiplication between elements is possible.
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On probabilistic norm of a linear operators and space of operators
Applied Mathematics and Mechanics, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Basics of Hilbert Space and Linear Operators
1991Show that a finite set {x1,..., x n } of n vectors in a Hilbert space H is linearly independent if and only if the n × n matrix that has 〈x j , x k 〉in the (j, k) position is non-singular.
Richard Kadison, John Ringrose
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Orthogonalities in linear spaces and difference operators
Aequationes Mathematicae, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1987
Matrix theory can be studied with no mention of linear spaces, and most of the results in this book are of such a nature. However, the introduction of linear spaces and the role of matrices in defining or representing linear transformations on such spaces add considerably to our insight.
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Matrix theory can be studied with no mention of linear spaces, and most of the results in this book are of such a nature. However, the introduction of linear spaces and the role of matrices in defining or representing linear transformations on such spaces add considerably to our insight.
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Fuzzifying topologies on the space of linear operators
Fuzzy Sets and Systems, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the position of the space of representable operators in the space of linear operators
1997The author studies complementability of the space \(R(L^1 (\lambda),Y)\) of representable operators in the space of all bounded operators \(L(L^1 (\lambda),Y)\). It is given a number of examples when \(R(L^1 (\lambda),Y)\) is complemented in \(L(L^1 (\lambda),Y)\), extending the known case \(Y=L^1 (\mu)\). For instance, when \(Y\) is a predual of a \(W^
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Bounded Linear Operators On a Hilbert Space
2002Everyone is familiar with linear operators. Multiplication by a constant is a linear operator. Multiplication of vectors by matrices generates an operator. Integration usually generates another, depending upon the setting.
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Linear Operators in Hilbert Spaces
2018We recall some fundamental notions of the theory of linear operators in Hilbert spaces which are required for a rigorous formulation of the rules of Quantum Mechanics in the one-body case. In particular, we introduce and discuss the main properties of bounded and unbounded operators, adjoint operators, symmetric and self-adjoint operators, self ...
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Decomposition of Linear Operators on Pre-Euclidean Spaces by Means of Graphs
Mathematics, 2023Elisabete Barreiro +2 more
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