Zeros and mapping theorems for perturbations of m-accretive operators in Banach spaces

✍ Scribed by R.P. Agarwal; Haiyun Zhou; Yeol Je Cho; Shin Min Kang

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 401 KB
• Volume: 49
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2005.01.012

✦ Synopsis

Let X be a real Banach space and T : D(T) C X --\* 2 X be an m-accretive operator. Let C : D(T) C X --~ X be a bounded operator (not necessarily continuous) such that C(T -+-i)-1 is compact. Suppose that for every x • D(T) with Hxll > r, there exists jx 6 Jx such that > o, (,) for all u E Tx. Then, we have 0 • (T + C)(D(T) N Br(0)), where B,(O) denotes the open ball of X with centre at zero and radius r > 0. Assume, furthermore, that T : D(T) --~ 2 X is strongly accretive. Then, 0 E (T + C)(D(T) n B~(0)). As applications of the above zero theorem, we derive many new mapping theorems for perturbations of m-accretive operators in Banach spaces. When, T and C are odd operators, we also obtain some new mapping theorems. @