id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-2952	Hamad, Safa L. ; Jamil, Zeana Z. 	The Completion of Generalized 2-Inner Product Spaces	2023	7	.pdf	application/pdf	2997	158	79	36(1)2023 317 Thus, by (5) and (6) we get ‖�̂�1 − �̂�2‖�̂� = lim 𝑛→∞ ‖�̂�1𝑛 − �̂�2𝑛‖𝑏 = lim 𝑛→∞ ‖�̂�1𝑛 − �̂�2𝑛‖𝑏 = ‖�̂�1 − �̂�2‖�̂� It implies that Ŵ is isometric to Ŷ.∎ 4. Thus, by equation (4) |‖�̂�1 − �̂�2‖�̂� − ‖�̂�1𝑛 − �̂�2𝑛‖𝑏| ≤ ‖�̂�1 − �̂�1𝑛‖𝑏 − ‖�̂�2 − �̂�2𝑛‖𝑏 → 0 By taking n → ∞ ‖�̂�1 − �̂�2‖�̂� = lim 𝑛→∞ ‖�̂�1𝑛 − �̂�2𝑛‖𝑏 (5) by the same argument ‖�̂�1 − �̂�2‖�̂� = lim 𝑛→∞ ‖�̂�1𝑛 − �̂�2𝑛‖𝑏 (6) IHJPAS.	cache/iajs-2952.pdf	txt/iajs-2952.txt