Definition df-bdop 28085

Description: Define the set of bounded linear Hilbert space operators. (See df-hosum 27973 for definition of operator.) (Contributed by NM, 18-Jan-2006.) (New usage is discouraged.)

Assertion

Ref	Expression
df-bdop	⊢ BndLinOp = {𝑡 ∈ LinOp ∣ (normop‘𝑡) < +∞}

Detailed syntax breakdown of Definition df-bdop

Step	Hyp	Ref	Expression
1		cbo 27189	. 2 class BndLinOp
2		vt	. . . . . 6 setvar 𝑡
3	2	cv 1474	. . . . 5 class 𝑡
4		cnop 27186	. . . . 5 class normop
5	3, 4	cfv 5804	. . . 4 class (normop‘𝑡)
6		cpnf 9950	. . . 4 class +∞
7		clt 9953	. . . 4 class <
8	5, 6, 7	wbr 4583	. . 3 wff (normop‘𝑡) < +∞
9		clo 27188	. . 3 class LinOp
10	8, 2, 9	crab 2900	. 2 class {𝑡 ∈ LinOp ∣ (normop‘𝑡) < +∞}
11	1, 10	wceq 1475	1 wff BndLinOp = {𝑡 ∈ LinOp ∣ (normop‘𝑡) < +∞}

This definition is referenced by:  elbdop  28103  hhbloi  28145