Do not expect reciprocity. Open your home in an attitude of non-expectation. Try not to hope.
This state is impossible for human beings. Recognize this impossibility and forgive yourself for your desire.
Yet continue to strive. Turn yourself inside out as much as you can. Strain toward the perfection of absolute giving as a horizon, an asymptote.
Things you could give away that you might not have thought of: your couch. The suit you were married in. Extra pens you have lying around. Your undivided attention. A kidney.
But be wary of potlatch and all forms of competition. If a friend doesn't want your kidney then don't embarrass him by pressing.
Recognize that there are limits to the concept of hospitality, which is based on the notion that my home is separate from yours. Hospitality is a modern invention and the bailiwick of the middle class; the mansions of the nobility were open by fiat to the state, to soldiers, to ghosts, to the gentle nosiness of Mr and Mrs Gardiner and the dreamy rapacity of Elizabeth Bennett. Only those who are not forced to billet soldiers or admit vampires can be said to extend hospitality. Consider whether you think hospitality is enough.
Some examples of hospitality include: Everything Winnie-the-Pooh does. A bunch of episodes in The Odyssey. Lots of stuff from the Bible.
Some examples of non-hospitality: Polyphemus (don't eat your guests, even if they were not invited). The Lotus-Eaters (allow your guests to leave when they want to). Circe (do not transform your guests into beasts). Odysseus and the suitors (however, also a grey area). Come to think of it, The Odyssey is pretty ambivalent about hospitality.
Hospitality should be invisible. If you make a big deal about how generous you are and how open your home, you undermine the whole enterprise. One of the best things Miss Manners ever advised was what to do if your guest accidentally drinks the contents of her finger bowl: immediately pick up your own finger bowl and down it.
Yet do not hide your light under a bushel simply to make others comfortable. Fakery of any kind is counter to the spirit of hospitality.
When friends tell you that they can't return your hospitality because your cooking is too delicious or the paintings on your walls are too beautiful and they feel ashamed, understand that they're being ridiculous. Forgive them and love them for being ridiculous.
Invite them over again soon and serve them a terrine of pressed butterfly wings in rosewater aspic. Feed them by hand.
Let them doze off on the couch, then depart your house as quietly as you can. Leave the keys on the front hall table. Take up residence in their tiny apartment and fall in love with their cruel cats and enjoy their tinned vegetables and stare at their framed movie posters until they move you to tears. Make a new furrow in their mattress. Forget your own name.