Communications of the Korean Mathematical Society (대한수학회논문집)
- Volume 9 Issue 3
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- Pages.593-598
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- 1994
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
THE JUMP OF A SEMI-FREDHOLM OPERATOR
- Lee, Dong-Hak (Department of Mathematics, Kang Won University, Choon Chun 200-701) ;
- Lee, Woo-Young (Department of Mathematics, Sung Kyun Kwan University, Suwon 440-746)
- Published : 1994.07.01
Abstract
In this note we give some results on the jump (due to Kato [5] and West [7]) of a semi-Fredholm operator. Throughout this note, suppose X is an Banach space and write L(X) for the set of all bounded linear operators on X. A operator $T \in L(x)$ is called upper semi-Fredholm if it has closed range with finite dimensional null space, and lower semi-Fredholm if it has closed range with its range of finite co-dimension. It T is either upper or lower semi-Fredholm we shall call it semi-Fredholm and Fredholm it is both. The index of a (semi-) Fredholm operator T is given by $$ index(T) = n(T) = d(T),$$ where $n(T) = dim T^{-1}(0)$ and d(T) = codim T(X).
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