Is xmlns="" a valid xml namespace?

It is not a valid XML NS. It is not a valid XML NS declaration. Please check section 2.2 of Namespaces in XML 1.0 :

The empty string, though it is a legal URI reference, cannot be used as a namespace name.

It is however the only way to undeclare a default NS declaration if there is one in effect, or it has no effect. See Namespaces in XML 1.0 and 1.1, section 6.2. The 1.1 NS rec added a way to also undeclare a NS declaration with a prefix.

Thus it is a valid value for the xmlns special attribute, but it is not "a valid XML namespace" like the OP wrote it.

Yes, it is valid. Section 6.2 in the Namespaces in XML 1.0 Recommendation specifically says:

The attribute value in a default namespace declaration MAY be empty. This has the same effect, within the scope of the declaration, of there being no default namespace.

Quoted from comment:

It is legal, and this is the way to bring an element into the global namespace.