ABSTRACT
CTIlI(A) = CTll1II(A) Up: ~ E CT(A), 0 ~ ind (A - ~I) < oo}j they are caJIed the essential spectrum of A in the sense of KATO (1966], WOLF [1959], and SCHECHTER [1965], respectively. Moreover, a point AE CT(A) belongs to the essentia.lspedrum CTe6(A) in the sense of BROWDER [1960] if either the range of A - ~I is not closed, or Ais an accumulation point of CT(A), or ~ is an eigenvalue of A of infinite multiplicity. Thus, ~ ¢ CTll1II (A) means that A - ~I is Fredholm, ~ ¢ CTe,(A) means that A - ~I is Fredholm of index zero, and ~ ¢ CTe6(A) means that ~ is an isolated eigenvalue of finite multiplicity. All sets mentioned above are closed subsets of CT(A), hence compact. For further reference, we recaJI some relations between these subsets (see e.g. KATO [1966], KREJN [1971] or ISHINOSE [1978, 1978a]).
