Definition df-bdop 9899

Description: Define the set of bounded linear Hilbert space operators. (See df-hosum 9637 for definition of operator.)

Assertion

Ref	Expression
df-bdop	|- BndLinOp = (LinOp i^i {t | (t:H~-->H~ /\ (normop` t) < +oo)})

Detailed syntax breakdown of Definition df-bdop

Step	Hyp	Ref	Expression
1		cbo 8997	. 2 class BndLinOp
2		clo 8996	. . 3 class LinOp
3		chil 8968	. . . . . 6 class H~
4		vt	. . . . . . 7 set t
5	4	cv 1098	. . . . . 6 class t
6	3, 3, 5	wf 3141	. . . . 5 wff t:H~-->H~
7		cnop 8994	. . . . . . 7 class normop
8	5, 7	cfv 3145	. . . . . 6 class (normop` t)
9		cpnf 5406	. . . . . 6 class +oo
10		clt 5409	. . . . . 6 class <
11	8, 9, 10	wbr 2587	. . . . 5 wff (normop` t) < +oo
12	6, 11	wa 223	. . . 4 wff (t:H~-->H~ /\ (normop` t) < +oo)
13	12, 4	cab 1440	. . 3 class {t | (t:H~-->H~ /\ (normop` t) < +oo)}
14	2, 13	cin 2017	. 2 class (LinOp i^i {t | (t:H~-->H~ /\ (normop` t) < +oo)})
15	1, 14	wceq 1099	1 wff BndLinOp = (LinOp i^i {t | (t:H~-->H~ /\ (normop` t) < +oo)})

This definition is referenced by:  dfbdop2 9917

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