# Direct product of Hilbert spaces

I know of direct sum in the category of Hilbert spaces. Is there a concept of direct product too, wherein one can consider arbitrary tuples ? (looks like a no, as in order to talk about convergence etc, one would need countably many non zero vectors)

• Do you mean $H \times H$? – Meowdog Feb 23 at 16:19
• No, over arbitrary (possibly uncountable) index set – Anupam Feb 23 at 16:34