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People like to say that they are in a relationship because they are in Love and want to spend the rest of their lives together; yet, most relationships have at least one person in it because of fear.
Men are more independent in their thoughts and actions, while women are more willing to follow the ideas suggested by others.
However, most relationships don't even make it out of the beginning stages because most people don't even have a good and healthy reason to be in a relationship let alone know what they are in a relationship for.
For complex vector spaces, the condition symmetric should be replaced by balanced
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.
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. "No you can't, either."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?