id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5587	Rashid, Mohammad H.M.; Alnabulsi, Salam 	On the Closability of Class Totally Paranormal Operators	2025	20	.pdf	application/pdf	8409	761	83	On H = ker(T − µI)⊕ ker(T − µI)⊥, T − µI can be decomposed as T − µI = [ 0 T12 0 T22 − µI|ker(T−µI)⊥ ] , where T22 = P |ker(T−µI)⊥T |ker(T−µI)⊥ . T is called totally paranormal [22] if T − µI is paranormal for every µ ∈ C. That is, ∥(T − µI)x∥2 ≤∥∥(T − µI)2x ∥∥ ∥x∥ for all x ∈ X and µ ∈ C.	cache/ejpam-5587.pdf	txt/ejpam-5587.txt