table for one please?

That's an excellent question. I see that you are from Spain (wonderful!), so people's attitudes might be different there than they are here. How much intimacy one prefers depends on the kind of restaurant it is, the time of the day, etc. If it's a busy lunch spot, this may happen often, and people might prefer to be left alone. If it's a more casual place, then they may feel comfortable being approached, but I don't think one should ever assume this. If it's a woman, it's important to make her feel that she is given equal treatment, and maybe even special consideration if she happens to be seated next to routy boys.

A couple of months ago, I had dinner at L'Atelier de Joel Robuchon in Paris. By myself. The restaurant only has bars, no tables. Like it or not, you will have to be sociable with your neighbours at some point in the evening. The hostess sat me at a counter which was empty except for a family. She sat me right next to them. It was awkward because I felt squished against them on my right, even though the whole bar on my left was completely empty. I asked if I could move to give these nice folks some privacy, but was told not to worry, and that the bar was all reserved in any case.

As the evening progessed, new people came in, and I was now flanked by strangers on both sides. But they were family types, very nice people who were kind without being obtrusive, and I ended up enjoying their company very much. Keep in mind, this is Robuchon customers, not half drunk pub customers... Not that there's anything wrong with being half drunk in a pub. :D

In a way, the company was so good that it took my focus away from the food; afterall, I came for the food not the company. Do I regret this? Not really. It was a spectacular evening.

The situation was different here than in your case, because you obviously have tables in your restaurant. I think to deliberately isolate a patron is inapropriate, but to respect their privacy is also key. Basically, don't have them facing a blank wall. I think it's nice that you speak to them; I can't imagine any circumstance where this would not be appreciated.

I disliked sitting alone when I was younger. I felt really self-conscious and often resorted to bringing a magazine or newspaper along to shift my focus. As I grew older I mellowed out and just enjoy watching the people (but not too obviously!). I try to guess who they are, what their stories are, etc. It's a fun, harmless diversion that I get to indulge in rarely these days.

I agree with Anneke: it varies by person. Perhaps a good question would be, "Do you have a preference for seating?" when you are able to offer such a choice. That way the diner can take the lead.

you shouldn't worry about it. If people disliked eating on their own in a restaurant they would avoid it. I am basically lazy when it comes to cooking for myself at home and eat out a lot with or without other people. It never occurred to me to be uncomfortable about it. I'm happy to be somewhere I can just read, or watch people and have my food served to me. I'm sure there's plenty others like me.

Jane mentioned:
On the whole, this is probably true, but I wouldn't count on it. I've had friends who were on business trips alone where room service was too awful to contemplate and dined at a restaurant by themselves very reluctantly. I think women are sometimes even more concerned. Getting hit-on or getting those pitying looks can really spoil an evening. But if a restaurant has a friendly atmosphere, if the diner is not exiled to a table behind a potted plant, and if the FOH folks don't treat him/her like a problem or an inconvenience, then nothing special needs to be done.

By the way, Lins, you sound like a wonderful chef in terms of the way you care about the experience of your customers. And trying out dining alone sounds like a great way to see what it's like. Just be sure to go somewhere they don't know you. :D

It's nice to meet such a thoughtful chef! Many managers think that a lone diner is a 50% waste of table...Kudos to you!