Definition df-bdop 28829

Description: Define the set of bounded linear Hilbert space operators. (See df-hosum 28717 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 27933	. 2 class BndLinOp
2		vt	. . . . . 6 setvar 𝑡
3	2	cv 1522	. . . . 5 class 𝑡
4		cnop 27930	. . . . 5 class normop
5	3, 4	cfv 5926	. . . 4 class (normop‘𝑡)
6		cpnf 10109	. . . 4 class +∞
7		clt 10112	. . . 4 class <
8	5, 6, 7	wbr 4685	. . 3 wff (normop‘𝑡) < +∞
9		clo 27932	. . 3 class LinOp
10	8, 2, 9	crab 2945	. 2 class {𝑡 ∈ LinOp ∣ (normop‘𝑡) < +∞}
11	1, 10	wceq 1523	1 wff BndLinOp = {𝑡 ∈ LinOp ∣ (normop‘𝑡) < +∞}

This definition is referenced by:  elbdop  28847  hhbloi  28889