Both Uses of

hypnotize
in
Arrowsmith

He used thought-forms, will-power, and hypnotism, and when he rose, defeated, she was still there, extremely placid.†
Chpt 5 *

hypnotism = the act of putting someone into a trance-like state of focused concentration and heightened suggestibility (a state of hypnosis)

While Novak bellowed into the farmline telephone in the dining-room, Martin waited—waited—staring at the child; Mrs. Novak waited for him to do miracles; the child's tossing and hoarse gasping became horrible; and the glaring walls, the glaring lines of pale yellow woodwork, hypnotized him into sleepiness.†
Chpt 15

Definitions:

(1) (hypnotize as in: hypnotized to try to remember)
to put someone into a state of hypnosis (a trance-like state of focused concentration and heightened suggestibility)

(Heightened suggestibility means that the hypnotized person is more inclined to accept and act on suggestions of the hypnotist.)
(2) (hypnotize as in: hypnotized by her performance)
fascinate so much that awareness of other surrounding things is lost or too much trust is granted
(3) (meaning too rare to warrant focus)
meaning too rare to warrant focus