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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)

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

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