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السلام عليكم
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bounded linear operator is a linear transformation L between normed vector spaces X and Y for which the ratio of the norm of L(v) to that of v is bounded by the same number, over all non-zero vectors v in X. In other words, there exists some M > 0 such that for all v in X,
The smallest such M is called the operator norm of L.

 

J. Dieudonné History of Functional Analysis
North Holland | 1983-01-01 | ISBN: 0444861483 | 312 pages | Djvu | 2,3 MB
North-Holland Mathematics Studies

 

Albrecht Pietsch, "History of Banach Spaces and Linear Operators" Birkhäuser Boston | 2007-04-11 | ISBN: 0817643672 | 855 pages | PDF | 5,1 MB






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