From Longman Dictionary of Contemporary Englishlook/stare/gaze into spacelook/stare/gaze into spaceLOOK ATto look straight in front of you without looking at anything in particular, usually because you are thinking → space
Examples from the Corpus
look/stare/gaze into space• Usually, after a performance I come home and stare into space.• Mrs Frizzell gazed into space and Mrs Murphy smoothed back errant curls from her damp forehead.• He was just gazing into space.• Mrs James caught me staring into space twice even though the girl sitting next to me had nudged me in time.• In his study, Bernard Quex stared into space, pen motionless over his notepad.• Rachel screamed and woke up, drenched with sweat, shaking, staring into space.• My companion remained oblivious to the sights, staring into space and frowning.• Sometimes the door was ajar and I would see her sitting absolutely still, staring into space, not reading at all. 