Results 141 to 150 of about 373,665 (180)
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2011
A linear operator A on a Hilbert space X is said to be a bounded linear operator on X if there exists a positive constant C such that $$||A_x|| \geq C||x||,\quad x \in X.$$
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A linear operator A on a Hilbert space X is said to be a bounded linear operator on X if there exists a positive constant C such that $$||A_x|| \geq C||x||,\quad x \in X.$$
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Bounded and Unbounded Linear Operators
2011This chapter is devoted to the basic material on operator theory, semigroups, evolution familites, interpolation spaces, fractional powers of operators, intermediate spaces, and their basic properties needed in the sequel. Various illustrative examples are discussed in-depth. The estimates in Lemma 2.2 (Diagana et al. [52]) and Lemma 2.4 (Diagana [62])
Paul H. Bezandry, Toka Diagana
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Representation of Bounded Linear Operators
2013In this final chapter we make a start on the difficult problem of representing linear maps (between Banach spaces) that are merely bounded. The magnitude of the task is underscored by the fact that even in a Hilbert space context, really satisfactory results are available only for normal operators. Moreover, the methods used in the spectral analysis of
David E. Edmunds, W. Desmond Evans
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INTUITIONISTIC FUZZY BOUNDED LINEAR OPERATORS
2007The object of this paper is to introduce the notion of intuitionistic fuzzy continuous mappings and intuitionistic fuzzy bounded linear operators from one intuitionistic fuzzy n-normed linear space to another. Relation be- tween intuitionistic fuzzy continuity and intuitionistic fuzzy bounded linear operators are studied and some interesting results ...
Vijayabalaji, S., Thillaigovindan, N.
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Linear extension operators of bounded norms
Journal of Mathematical Analysis and Applications, 2018Abstract Dugundji spaces were introduced by Pelczynski as compact Hausdorff spaces X such that every embedding of X into a Tychonoff cube [ 0 , 1 ] A admits a linear extension operator u : C ( X ) → C ( [ 0 , 1 ] A ) such that ‖ u ‖ = 1 and u ( 1 X ) = 1 [ 0 , 1 ] A
Dmitri Shakhmatov +2 more
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On Certain Classes of Bounded Linear Operators
Canadian Mathematical Bulletin, 1970Let T—c be a Fredholm operator, where T is a bounded linear operator on a complex Banach space and c is a scalar, the set of all such scalars is called the Φ-set of T [2] and was studied by many authors. In this connection, the purpose of the present paper is to investigate some classes Φ(V) of all such operators for any subset V of the complex plane ...
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Bounded and Unbounded Linear Operators
1987Let H be a complex inner product space and let L(H) be the set of all bounded linear operators on H. In this chapter we present some basic facts about the set L(H) as well as about the set of unbounded operators on H. We also present some classes of operators whose structure is better understood, among which we mention the class of hermitian, unitary ...
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