The Vedanta Sutras, commentary by Sankaracharya (SBE34), tr. by George Thibaut  at sacred-texts.com
9. And on account of the agreement of the attributes (mentioned in the text).
The attributes, moreover, which the sacred text ascribes to the bhûman agree well with the highest Self. The passage, 'Where one sees nothing else, hears nothing else, understands nothing else, that is the bhûman,' gives us to understand that in the bhûman the ordinary activities of seeing and so on are absent; and that this is characteristic of the highest Self, we know from another scriptural passage, viz. 'But when the Self only is all this, how should he see another?' &c. (Bri. Up. IV, 5, 15). What is said about the absence of the activities of seeing and so on in the state of deep sleep (Pra. Up. IV, 2) is said with the intention of declaring the non-attachedness of the Self, not of describing the nature of the prâna; for the highest Self (not the vital air) is the topic of that passage. The bliss also of which Scripture speaks as connected with that state is mentioned only in order to show that bliss constitutes the nature of the Self. For Scripture says (Bri. Up. IV, 3, 32), 'This is his highest bliss. All other creatures live on a small portion of that bliss.'--The passage under discussion also ('The bhûman is bliss. There is no bliss in that which is little (limited). The bhûman only is bliss') by denying the reality of bliss on the part of whatever is perishable shows that Brahman only is bliss as bhûman, i.e. in its plenitude,--Again, the passage, 'The bhûman is immortality,' shows that the highest cause is meant; for the immortality of all effected things is a merely relative one,
and another scriptural passage says that 'whatever is different from that (Brahman) is perishable' (Bri. Up. III, 4, 2).--Similarly, the qualities of being the True, and of resting in its own greatness, and of being omnipresent, and of being the Self of everything which the text mentions (as belonging to the bhûman) can belong to the highest Self only, not to anything else.--By all this it is proved that the bhûman is the highest Self.