Theorem bdopssadj

Description: Every bounded linear Hilbert space operator has an adjoint. (Contributed by NM, 19-Feb-2006) (New usage is discouraged.)

	Ref	Expression
Assertion	bdopssadj	$$⊢\mathrm{BndLinOp}\subseteq \mathrm{dom}{adj}_h$$

Proof

Step	Hyp	Ref	Expression
1		lncnbd	$$⊢\mathrm{LinOp}\cap \mathrm{ContOp}=\mathrm{BndLinOp}$$
2		cnlnssadj	$$⊢\mathrm{LinOp}\cap \mathrm{ContOp}\subseteq \mathrm{dom}{adj}_h$$
3	1 2	eqsstrri	$$⊢\mathrm{BndLinOp}\subseteq \mathrm{dom}{adj}_h$$