Bernstein Polynomials as Linear Operators

Jorge Bustamante
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Jorge Bustamante: Benemerita Universidad Autonoma de Puebla, Facultad de Ciencias Físico-Matemáticas

Chapter Chapter 3 in Bernstein Operators and Their Properties, 2017, pp 161-173 from Springer

Abstract: Abstract Recall that, if (X, ∥ ∘ ∥ X ) and (Y, ∥ ∘ ∥ Y ) are normed spaces and L: X → Y is a continuous linear operator, then the norm of L is defined as ∥ L ∥ X → Y = sup { ∥ L ( x ) ∥ Y : ∥ x ∥ X ≤ 1 } . $$\Vert L\Vert _{X\rightarrow Y } =\sup \{\Vert L(x)\Vert _{Y }\,:\,\Vert x\Vert _{X} \leq 1\}.$$ Moreover, a linear operator L: X → Y is continuous if and only if ∥ L ∥ X → Y

Date: 2017
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DOI: 10.1007/978-3-319-55402-0_3

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