"Ship up to back! Ting-a-ling-ling!" His arms straightened and stiffened down his sides."Set her back on the stabboard! Ting-a-ling-ling! Chow! ch-chow-wow! Chow!" His right hand, mean- time, describing stately circles -- for it was representing a forty-foot wheel.
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Instead of using arbitrary Banach spaces and nuclear operators, we can give a definition in terms of Hilbert spaces and trace class operators, which are easier to understand. (On Hilbert spaces nuclear operators are often called trace class operators.) We will say that a seminorm p is a Hilbert seminorm if Vp is a Hilbert space, or equivalently if p comes from a sesquilinear positive semidefinite form on V.
A nuclear space is a topological vector space with a topology defined by a family of Hilbert seminorms, such that for any Hilbert seminorm p we can find a larger Hilbert seminorm q so that the natural map from Vq to Vp is trace class.
I love you, and I do not want this to ruin our relationship.
I want to spend the rest of my life with you, but I need you to listen to me more...
For any seminorm, the unit ball is a closed convex symmetric neighborhood of 0
But I must explain to you how all this mistaken idea of denouncing pleasure and praising pain was born and I will give you a complete account of the system, and expound the actual teachings of the great explorer of the truth, the master-builder of human happiness. "She'd never noticed if it hadn't been for Sid. Confound it! sometimes she sews it with white, and sometimes she sews it with black. I wish to gee- miny she'd stick to one or t'other -- I can't keep the run of 'em. But I bet you I'll lam Sid for that. I'll learn him!"No one rejects, dislikes, or avoids pleasure itself, because it is pleasure, but because those who do not know how to pursue pleasure rationally encounter consequences that are extremely painful. Nor again is there anyone who loves or pursues or desires to obtain pain of itself, because it is pain, but because occasionally circumstances occur in which toil and pain can procure him some great pleasure. To take a trivial example, which of us ever undertakes laborious physical exercise, except to obtain some advantage from it? But who has any right to find fault with a man who chooses to enjoy a pleasure that has no annoying consequences, or one who avoids a pain that produces no resultant pleasure?